Significant Number Factoid Friday – Today The Number Is Sixty-Four 64

“Fight Against Stupidity And Bureaucracy”

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Another significant numbers day.

In case you are wondering these numbers are picked quite randomly. Only after it makes itself known does the search start for things associated with it.

Sometimes there is a lot, sometimes not so much. Sixty-four seems to be a well used number so a lot of information below.

If you are into numbers, enjoy.

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The Number Sixty-Four  64

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In religion

• The 64th word of the King James Version of the Bible’s Old Testament Genesis is “light”;
• King David prays for deliverance from his enemies in the 64th Psalm;
• The 64 Dakinis or Yoginis are 8 Mother goddesses each with 8 attendants in India religious traditions; each of the 64 can be further correlated to the currents or winds of the human “etheric” body;
• The Lord Shiva has 64 forms or manifestations.

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In mathematics

• Sixty-four is the square of 8, the cube of 4, and the sixth power of 2;
• Sixty-four is the smallest number with exactly seven divisors;
• Sixty-four is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime;
• Sixty-four  is the sum of Euler’s totient function for the first fourteen integers;
• Sixty-four is also a dodecagonal number and a centered triangular number;
• In base 10, no integer added up to its own digits yields 64, hence it is a self number;
• Sixty-four is a super-perfect number – a number such that s(s(n))=2n.

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• Base64
• Base64 is a group of similar binary-to-text encoding schemes that represent binary data in an ASCII string format by translating it into a radix-64 representation. The term Base64 originates from a specific MIME content transfer encoding.
• Base64 encoding schemes are commonly used when there is a need to encode binary data that needs to be stored and transferred over media that are designed to deal with textual data. This is to ensure that the data remain intact without modification during transport.
• Base64 is commonly used in a number of applications including email via MIME, and storing complex data in XML.

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• Graham’s number
• Graham’s number, named after Ronald Graham, is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes’ number and Moser’s number.
• The number gained a degree of popular attention when Martin Gardner described it in the “Mathematical Games” section of Scientific American in November 1977, writing that, “In an unpublished proof, Graham has recently established … a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof.” The 1980 Guinness Book of World Records repeated Gardner’s claim, adding to the popular interest in this number.
• Specific integers known to be far larger than Graham’s number have since appeared in many serious mathematical proofs (e.g., in connection with Friedman’s various finite forms of Kruskal’s theorem).

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In Computing

• 64-bit
• In computer architecture, 64-bit computing is the use of processors that have datapath widths, integer size, and memory addresses of 64 bits (eight octets) wide. Also, 64-bit CPU and ALU architectures are those that are based on registers, address buses, or data buses of that size. From the software perspective, 64-bit computing means the use of code with 64-bit virtual memory addresses

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• Commodore 64
• The Commodore 64, commonly called C64, CBM 64 (for Commodore Business Machines), or VIC-64, is an 8-bit home computer introduced in January 1982 by Commodore International.
• Volume production started in the spring of 1982, with machines being released on to the market in August at a price of US$595.
• Preceded by the Commodore VIC-20 and Commodore PET, the C64 took its name from its 64 kilobytes (65,536 bytes) of RAM, and had favorable sound and graphical specifications when compared to contemporary systems such as the Apple II, at a price that was well below the circa US$ 1200 demanded by Apple.
• For a substantial period (1983–1986), the C64 dominated the market with between 30% and 40% share and 2 million units sold per year, outselling the IBM PC compatibles, Apple Inc. computers, and Atari 8-bit family computers.
• Sam Tramiel, a later Atari president and the son of Commodore’s founder, said in a 1989 interview “When I was at Commodore we were building 400,000 C64s a month for a couple of years.”

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• Dragon 64
• The Dragon 32 and Dragon 64 are home computers that were built in the 1980s. The Dragons are very similar to the TRS-80 Color Computer (CoCo), and were produced for the European market by Dragon Data, Ltd., in Port Talbot, Wales, and for the US market by Tano of New Orleans, Louisiana.
• The model numbers reflect the primary difference between the two machines, which have 32 and 64 kilobytes of RAM, respectively.

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In science

• Sixty-four is the Atomic Number of Gadolinium (Gd), discovered by Jean de Marignac 1880 (Switzerland), and named after the mineral gadolinite;
• Sixty-four is the Atomic Weight of Copper (Cu).
• There are 64 codons in the RNA codon table under genetic code.

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In space

• Messier object M64, is a magnitude 9.0 galaxy in the constellation Coma Berenices, also known as the Black Eye Galaxy;
• The New General Catalogue object NGC 64, a barred spiral galaxy in the constellation Cetus;
• WOH G64 is a red hypergiant in the Large Magellanic Cloud. With 1540 times the radius of the Sun, it is one of the largest known stars and the largest known in the LMC. The physical parameters are still poorly known due to the distance, visual faintness, several solar masses of shrouding dust, and the possibility of a bright hot companion.

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• STS-64
• STS-64 was a Space Shuttle Discovery mission, launched from Kennedy Space Center, Florida, on 9 September 1994, to perform multiple experiment packages.
• STS-64 marked the first flight of Lidar In-space Technology Experiment (LITE) and first untethered U.S. extravehicular activity (EVA) in 10 years. LITE payload employs lidar, which stands for “light detection and ranging”, a type of optical radar using laser pulses instead of radio waves to study Earth’s atmosphere.
• On day five of the mission, the Shuttle Pointed Autonomous Research Tool for Astronomy-201 (SPARTAN-201) free flyer was released using the Remote Manipulator System arm.
• STS-64 was the first mission to see the use of the new full-pressure Advanced Crew Escape Suit, which eventually replaced the partial-pressure Launch Entry Suit.

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In politics

• Department of State Form DS-64 is the one US Citizens need if they lose or have your passport stolen;
• Department of Labor Chapter 64 regulates the employment of workers with disabilities at special wages;
• In the United States presidential election of 1964, held on Tuesday, November 3, 1964, Democratic candidate and incumbent President Lyndon B. Johnson who had come to office less than a year earlier following the assassination of his predecessor, John F. Kennedy, and who had successfully associated himself with Kennedy’s popularity, won 61.1% of the popular vote, the highest won by a candidate since 1820.

• In Chinese the “Six Four Incident” refers to Tiananmen Square protests of 1989.

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In sport

• There are 64 teams participating in the NCAA Basketball Tournament;
• In chess or draughts, there are a total of 64 black (dark) and white (light) squares on the game board;
• The Knight’s Tour of a chessboard is a sequence of moves by a knight so that each of the 64 squares is visited only once. The numbers of the knight’s moves form a magic square where each row and column adds up to 260;
• 64 is the name of the premier Russian chess magazine;
• NFL Hall of Famers with jersey #64 include Dave Wilcox, Linebacker (Boise Junior College, Oregon) and 1964-1974 San Francisco 49ers; George Blanda, Quarterback-Kicker, 1949, 1950-58 Chicago Bears, 1950 Baltimore Colts, 1960-66 Houston Oilers, 1967-1975 Oakland Raiders; Joe Delamielleure, Guard, 1973-1979, 1985 Buffalo Bills, 1980-1984 Cleveland Browns; Randall McDaniel, Guard, 1988-1999 Minnesota Vikings, 2000-01 Tampa Bay Buccaneers; Y.A. Tittle, Quarterback, 1948-1950 Baltimore Colts (AAFC/NFL), 1951-1960 San Francisco 49ers, 1961-1964 New York Giants.

• In the National Hockey League, jersey #64 is used by James Robert McGinn IV is a Canadian professional ice hockey player currently playing for the Colorado Avalanche.

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In books, movies, music and TV

• The $64,000 Question is an American game show broadcast from 1955–1958, which became embroiled in the scandals involving TV quiz shows of the day. The $64,000 Challenge (1956–1958) was its popular spin-off show.
• When I’m 64 is a song by John Lennon & Paul McCartney from The Beatles’ Sgt. Pepper’s Lonely Hearts Club Band album (1967).

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In militaria

• HMS Vansittart
• HMS Vansittart was an Admiralty modified W class destroyer built for the Royal Navy. She was ordered in January 1918 from William Beardmore & Company with the 13th Order for Destroyers of the Emergency War Program of 1918-19. She was the second Royal Navy ship to carry the name which was first used in 1821 for a hired packet.

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• HMS Beverley (H 64)
• Completed in July 1920 as USS Branch (DD 197) for the US Navy, on 8 Oct, 1940 she was transferred to the Royal Navy and renamed HMS Beverley (H 64).
• On 9 Apr, 1943, during WWII convoy duty in the North Atlantic, HMS Beverley had been seriously damaged in a collision with the British steam merchant Cairnvalona and had taken station in the rear of the convoy. When it was subsequenty attaced by a German U-Boat, U-188, 30 hours later she was hit by torpedos and sunk. HMS Clover (K 134) (Lt P.H. Grieves, RNR) later picked up five survivors and recovered two bodies, but one of the survivors later died on board.

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• HMS Fencer (D64)
• The USS Croatan (CVE-14) (originally AVG-14 then ACV-14) was transferred to the United Kingdom on 20 February 1943 under lend-lease where she served as HMS Fencer (D64). As an anti-submarine warfare carrier, Fencer escorted Atlantic, Russian and African convoys, even participating in a strike on the German battleship Tirpitz before being transferred to the Pacific.
• Following World War II, she returned to the United States 21 December 1946, stricken for disposal on 28 January 1947 and sold into merchant service 30 December as Sydney.
• The ship went through a series of renamings, first to Roma in 1967, then Galaxy Queen in 1970, Lady Dina in 1972 and finally Caribia in 1973 before being scrapped in Spezia in September 1975.

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• HMS Scorpion (D64)
• HMS Scorpion (D64) was a Weapon-class destroyer of the British Royal Navy. Originally named HMS Centaur, the ship was renamed Tomahawk and finally Scorpion (in September 1943) before her launch.
• Scorpion was the only Weapon-class ship fitted with the Limbo depth charge mortar rather than the older Squid.
• In 1953 she took part in the Fleet Review to celebrate the Coronation of Queen Elizabeth II.

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• HMS Theseus (R64)
• HMS Theseus (R64) was a Colossus-class light fleet aircraft carrier of the Royal Navy, launched on 6 July 1944.
• Theseus was laid down to serve in the Second World War, but was not completed before peace was declared in 1945. She was utilized as a training vessel until the outbreak of the Korean War when she was deployed to Korea, commencing standard carrier operations.
• In 1956, Theseus was used as an emergency commando carrier, along with her sister-ship Ocean, during the Suez Crisis. From November to December, helicopters from Theseus transported troops ashore, as well as evacuating wounded soldiers. Compared to her actions during the Korean War, her role at Suez was relatively quiet. The following year she was placed in reserve. She was subsequently broken up at Inverkeithing in 1962.

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• USS Wisconsin (BB-64)
• The USS Wisconsin (BB-64), “Wisky” or “WisKy”, is an Iowa-class battleship, the second ship of the United States Navy to be named in honor of the U.S. state of Wisconsin. She was launched on 7 December 1943 (the second anniversary of the Pearl Harbor raid).
• During her career, Wisconsin served in the Pacific Theater of World War II, where she shelled Japanese fortifications and screened United States aircraft carriers as they conducted air raids against enemy positions.
• During the Korean War, Wisconsin shelled North Korean targets in support of United Nations and South Korean ground operations, after which she was decommissioned.
• She was reactivated 1 August 1986, modernised and participated in Operation Desert Storm in January and February 1991.
• Wisconsin was last decommissioned in September 1991, having earned a total of six battle stars for service in World War II and Korea, as well as a Navy Unit Commendation for service during the January/February 1991 Gulf War.
• She currently functions as a museum ship operated by Nauticus, The National Maritime Center in Norfolk, Virginia. .

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• USS Constellation (CV-64)
• The USS Constellation (CV-64), a Kitty Hawk–class supercarrier, was the third ship of the United States Navy to be named in honor of the “new constellation of stars” on the flag of the United States and the only naval vessel ever authorized to display red, white, and blue designation numbers.
• One of the fastest ships in the Navy, as proven by her victory during a battlegroup race held in 1985, she was nicknamed “Connie” by her crew and officially as “America’s Flagship”.
• She was launched 8 October 1960 and delivered to the Navy 1 October 1961, and commissioned 27 October 1961, with Captain T. J. Walker in command. At that time, she had cost about US$264.5 million. Constellation was the last U.S. aircraft carrier (as of 2010) to be built at a yard other than Newport News Shipbuilding & Drydock Company.

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• USS Gettysburg (CG-64)
• The USS Gettysburg (CG-64) is a Ticonderoga-class guided-missile cruiser in the United States Navy, built at the Bath Iron Works in Maine and named for the Battle of Gettysburg during the American Civil War.
• With her guided missiles and rapid-fire cannons, she is capable of facing and defeating threats in the air, on the sea, or ashore, and underneath the sea. She also carries two Seahawk LAMPS multi-purpose helicopters, but mainly for anti-submarine warfare (ASW).
• She is based in Mayport, Florida.

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• U-64
• The first U-64 was a Type U-63 class submarine in the Kaiserliche Marine that served during World War I. She was built in 1916 and served in the Mediterranean Sea.
• On 19 March 1917, while on patrol in the Tyrrhenian Sea, U-64 torpedoed and sank the French battleship Danton 30 miles south of Sardinia, with the loss of 296 men. She herself was lost on 17 June 1918.

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• In 1937 another German submarine U-64, a Type IXB U-boat of the Nazi German Kriegsmarine, was ordered in July 1937 and launched in September 1939.
• This U-64 had a very short career and sank no enemy vessels. Having left her home port of Wilhelmshaven for her first war patrol on 6 April 1940, she was intercepted by Allied aircraft seven days later off the coast of Norway during the invasion of that country and was sunk by a bomb from a Fairey Swordfish aircraft of HMS Warspite. Of her crew of 46, eight men died and 38 escaped from the sinking submarine.

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• K-64
• The K-64 Designation was first given to the first Alfa Class Submarine, launched on April 22, 1969.
• In 1972, the submarine suffered a major reactor problem in the form of a leak of liquid metal coolant. The superheated metal solidified on contact with the colder outside air, freezing and damaging internal components of the reactor. She was removed from service and towed to Severodvinsk.
• The K-64 designation was again given to a Delta IV class submarine launched on February 2, 1986 as the fourth ship of its class, entered in service in the Russian Northern Fleet. The sub was laid down in December 1982 and was built at Sevmash plant in Severodvinsk.
• This ship is still in active service.

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• P-64
• P-64 was the designation assigned by the United States Army Air Corps (USAAC) to the North American Aviation NA-68 fighter, an upgraded variant of the NA-50 developed during the late 1930s.
• Six NA-68s ordered by the Royal Thai Air Force were seized before export by the US government in 1941, after the Franco-Thai War and growing ties between Thailand and the Empire of Japan. These aircraft were used by the USAAC as unarmed fighter trainers.
• Seven NA-50s were purchased by the Peruvian Air Force, which nicknamed it Torito (“Little Bull”). The Peruvian NA-50s subsequently saw action during the Ecuadorian-Peruvian War of 1941.

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• The Grumman G-64/111 Albatross
• The Albatross is easily the largest of Grumman’s series of utility amphibians, and was the only one originally developed specifically for military service.
• The Albatross resulted from a late 1940s US Navy requirement for a general purpose amphibious transport. The first Albatross prototype flew for the first time on October 24 1947, with more than 400 production HU-16s subsequently delivered to the US Navy, US Coast Guard and 12 other nations. Military Albatross missions included general reconnaissance, maritime patrol, anti submarine warfare (in which role it could be armed with torpedoes and depth charges) and search and rescue.
• In the late 1970s, Grumman and major US flying boat operator Resorts International began work on a program to convert the Albatross for civil airline service. The conversion incorporated numerous changes to the basic Albatross, including a 28 seat passenger interior, a galley and provision for a flight attendant, upgraded avionics and other improved systems.
• In all only 13 aircraft were converted, 12 for Resorts International, and 1 for Conoco Oil/Pelita which operated from Singapore. Several of these are still active, together with ex military examples.

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• AH-64 Apache
• The Boeing AH-64 Apache is a four-blade, twin-engine attack helicopter with a tailwheel-type landing gear arrangement, and a tandem cockpit for a two-man crew.
• Originally, the Apache started life as the Model 77 developed by Hughes Helicopters for the United States Army’s Advanced Attack Helicopter program to replace the AH-1 Cobra, and was first flown on 30 September 1975.
• The AH-64 was introduced to U.S. Army service in April 1986.
• The AH-64 Apache features a nose-mounted sensor suite for target acquisition and night vision systems; is armed with a 30-millimeter (1.2 in) M230 Chain Gun carried between the main landing gear, under the aircraft’s forward fuselage; and has four hardpoints mounted on stub-wing pylons, typically carrying a mixture of AGM-114 Hellfire missiles and Hydra 70 rocket pods. The AH-64 has a large amount of systems redundancy to improve combat survivability.
• The first production AH-64D Apache Longbow, an upgraded version of the original Apache, was delivered to the Army in March 1997. Production has been continued by Boeing Defense, Space & Security; over 1,000 AH-64s have been produced to date.
• The U.S. Army is the primary operator of the AH-64; it has also become the primary attack helicopter of multiple nations, including Greece, Japan, Israel, the Netherlands and Singapore; as well as being produced under license in the United Kingdom as the AgustaWestland Apache. U.S. AH-64s have served in conflicts in Panama, the Persian Gulf, Kosovo, Afghanistan, and Iraq. Israel used the Apache in its military conflicts in Lebanon and the Gaza Strip; both British and U.S. Apaches have seen deployments in Afghanistan and Iraq.

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• Sikorsky S-64 Skycrane
• The Sikorsky S-64 Skycrane is an American twin-engine heavy-lift helicopter, the civil version of the United States Army’s CH-54 Tarhe. The S-64 Aircrane is the current production version, manufactured by the Erickson Air-Crane company.
• Erickson Air-Crane purchased the type certificate and manufacturing rights in 1992 and since that date they have become the manufacturer and world’s largest operator of S-64 Aircranes. The Aircrane can be fitted with a 2,650-gallon (~10,000 litre) fixed retardant tank to assist in the control of bush fires, and it has proved itself admirably in this role.
• Erickson is manufacturing new S-64s, as well as remanufacturing existing CH-54s, with each being assigned an individual name, the best-known being “Elvis”, used in fighting fires in Australia alongside “The Incredible Hulk” and “Isabelle”.
• Other operators, such as Siller Brothers, have followed with their Sikorsky S-64E, Andy’s Pride. The Erickson S-64E nicknamed “Olga” was used to lift the top section of the CN Tower into place in Toronto, Canada.
• The S-64 is the first helicopter built with a rear-facing pilot’s seat—this allows the pilot to watch exactly where the load is being placed as he’s flying the helicopter. The feature came in handy in 1993, when an S-64 removed and replaced the Statue of Freedom from the US Capitol building during a renovation. When transporting a big load like that, the S-64 uses an anti-rotation rigging system that prevents the aircraft from twisting and swaying.

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• T-64
• The T-64 is a Soviet main battle tank, introduced in the early 1960s. It was a more advanced counterpart to the T-62: the T-64 served tank divisions, while the T-62 supported infantry in motor rifle divisions. Although the T-62 and the famed T-72 would see much wider use and generally more development, it was the T-64 that formed the basis of more modern Soviet tank designs like the T-80.

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• W64 nuclear warhead
• The W64 nuclear warhead was the Los Alamos Laboratory’s entry into a brief competition between Lawrence Livermore Laboratory and Los Alamos to design an “enhanced-radiation” nuclear warhead (i.e., a “neutron bomb”) for the United States Army’s MGM-52 Lance tactical surface-to-surface missile.
• The Los Alamos design, the W64, was canceled in September 1964 in favor of Livermore’s W63. In November 1966, the W63 was canceled in favor of the W70, the model that finally entered production.

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• L64
• The L64 was an intermediate calibre British bullpup layout prototype assault rifle developed in the 1970s. The British Army had considered bullpup designs with intermediate calibre rounds in the 1950s, and officially adopted one of these as .280 British in 1951 in the EM-2 and Taden gun. However, US intransigence during NATO standardization efforts, and Winston Churchill’s interest in standards above all, led to the adoption of the significantly more powerful 7.62×51mm NATO round and the British and Canadian armies adopted the L1A1 SLR, a licensed version of the FN FAL, itself originally designed for the .280.
• In the late 1960s a new L64/65 “Individual Weapon” was developed, outwardly similar to the earlier EM-2, but adopted a firing mechanism very similar to ArmaLite’s latest AR-18 design. The first examples were available in 1972.
• By 1976, NATO was ready to standardize on a small calibre round, and testing of the various rounds head-to-head started in 1977. As designed, the British round out-performed the standard US 5.56 mm. However Fabrique Nationale’s entry based on the 5.56 mm, the “SS-109” performed as well as the British cartridge. In the end it was selected largely due to its similarity with existing US ammunition.
• The L64 pattern was later developed into the SA80 family of weapons, which entered service with the UK in the 1980s.

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• P-64 Pistol
• The P-64 is a Polish 9mm semi-automatic pistol designed to fire the 9x18mm Makarov cartridge. The pistol was developed in the late 1950s at the Institute for Artillery Research, which later became the Military Institute of Armament Technology.

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In other fields

• Cities situated on longtitude 64 degree west are:  Charlotte Amalie,  US Virgin Islands; Hamilton,  Bermuda; Road Town,  British Virgin Islands; and Córdoba, Argentina.
• Cities situated on latitude 64 north are:  Fairbanks, Alaska; Skellefteå, Sweden; Anadyr and Arkhangelsk, Russia; Nuuk (Godthåb), Greenland; and Reykjavík, Iceland.
• There are 64 gems in total number in a standard Bejeweled game board.
• 64 is the code for international direct dial calls to New Zealand.
• There are 64 Braille characters in the old 6-dot system.
• Since 1996, the number 64 has been an abbreviation or slang for Nintendo 64 (though N64 is more common) along with the games Super Mario 64, Mario Kart 64 and more.

• 64 is the maximum number of strokes in any Chinese character.
• There are 64 hexagrams in the I Ching.
• There are 64 sexual positions in the Kama Sutra.
• There are 64 demons in the Dictionnaire Infernal.
• There are 64 classical arts listed in many Indian scriptures. They include: singing, dancing, painting, poetry, playing cards, making arguments, making flower garlands, etc.
• The 64th French department is Pyrénées-Atlantiques.
• Unsurprisingly it is the number of crayons in the popular Crayola 64 pack.
• 64 is the maximum stack size in the popular game Minecraft.
• 64 (dog) is a character in the Donald Duck comics universe.
• Number of golden disks in the myth of the Tower of Hanoi.
• The S64-1.25 MW has a well-suited ratio of rotor diameter to generator for most sites in a medium wind speed regime. The wind turbine concept is based on robust design and is efficiently handled by the Suzlon controller. These technologies are all well-known in the wind power industry and have proven themselves over time.

• PARALOID B-64 solid grade acrylic resin provides an outstanding combination of hardness, flexibility, and adhesion to various substrates. This general-purpose resin permits wider latitude in formulating in solvents that are suitable for specific applications.
• Group f/64 was a group of seven 20th century San Francisco photographers who shared a common photographic style characterized by sharp-focused and carefully framed images seen through a particularly Western (U.S.) viewpoint. In part, they formed in opposition to the Pictorialist photographic style that had dominated much of the early 20th century, but moreover they wanted to promote a new Modernist aesthetic that was based on precisely exposed images of natural forms and found objects.
• 64 is the slang term referring to a 1964 Chevrolet Impala, often configured as a lowrider, a popular subject among early-90’s gangsta rap.

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Significant Number Factoid Friday – Today The Number Is Twenty-One 21

“Fight Against Stupidity And Bureaucracy”

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Today a number that many people like and hold to be ‘lucky’.

The Number 21

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In religion

• Number of the perfection by excellence, 3 x 7, according to the Bible.
• 21 represents the harmony of the creation.
• Mary, mother of Jesus, lived 21 years after the death Jesus
• There were 21 years between the presentation of Jesus to the Temple at 12 years old and his death at 33 years old.
• In the same day, Jesus appears in 21 different places in Palestine to confirm in His Resurrection.
• The word angel is pronounced 21 times by Jesus, always to the plural.
• The words Flood and star are used 21 times in the Bible.
• In the Revelation, the word “capacity” (capacity of decision or to act, by opposition to “power”) is used 21 times.

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In mathematics

21 is a Triangular, Octagonal, Fibonacci, and Motzkin Number.

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In science & technology

• The Chemical Element Scandium has an atomic number of 21.
• There are 21 amino-acids.
• 21 is the standard TCP/IP port number for FTP connections

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In space and aviation

• Messier 21 or M21
• Messier 21 or M21 (also designated NGC 6531) is an open cluster of stars in the constellation of Sagittarius. It was discovered and catalogued by Charles Messier on June 5, 1764.
•  It is tightly packed but contains about 57 stars. A few blue giant stars have been identified in the cluster, but Messier 21 is composed mainly of small dim stars. With a magnitude of 6.5, M21 is not visible to the naked eye; however, with the smallest binoculars it can be easily spotted on a dark night.

 

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• Expedition 21
• Expedition 21 was the 21st long-duration mission to the International Space Station (ISS). The expedition began on 30 September 2009, with Frank de Winne becoming the first ESA astronaut to command a space mission.

• The handover between Expedition 20 and Expedition 21 required three Soyuz vehicles being docked to the station at the same time, the first time this has occurred.
• Soyuz TMA-16 brought the final members of Expedition 21 to the ISS, along with space tourist Guy Laliberté. Laliberté returned to Earth on Soyuz TMA-14 with two members of Expedition 20 on 11 October 2009.
• Nicole P. Stott was the last ISS expedition crew member to fly on the Space Shuttle. She returned to Earth aboard STS-129 in November 2009.

Expedition 21 crew portrait (from the left) are Flight Engineers Nicole Stott, Frank De Winne and Roman Romanenko. Pictured on the back row (from the left) are Flight Engineer Maxim Suraev, Commander Jeffrey Williams and Flight Engineer Robert Thirsk. Image credit: NASA

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• Luna 21
• Luna 21 (Ye-8 series) was an unmanned space mission of the Luna program, also called Lunik 21. The spacecraft landed on the Moon and deployed the second Soviet lunar rover (Lunokhod 2). The primary objectives of the mission were to collect images of the lunar surface, examine ambient light levels to determine the feasibility of astronomical observations from the Moon, perform laser ranging experiments from Earth, observe solar X-rays, measure local magnetic fields, and study mechanical properties of the lunar surface material.

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• Number 21
• Number 21 is the name of the plane alleged flown by Gustave Whitehead two years before the Wright brothers’ flight

 

 

In politics

• 21^st President of the United States
• Chester Alan Arthur (October 5, 1829 – November 18, 1886) was the 21st President of the United States (1881–85). He became President after the assassination of President James A. Garfield.
• Born in Fairfield, Vermont, Arthur grew up in upstate New York and practiced law in New York City. He devoted much of his time to Republican politics and quickly rose in the political machine run by New York Senator Roscoe Conkling.
• Appointed by President Ulysses S. Grant to the lucrative and politically powerful post of Collector of the Port of New York in 1871, Arthur was an important supporter of Conkling and the Stalwart faction of the Republican Party.
• In 1878 the new president, Rutherford B. Hayes, fired Arthur as part of a plan to reform the federal patronage system in New York. When James Garfield won the Republican nomination for President in 1880, Arthur was nominated for Vice President to balance the ticket by adding an eastern Stalwart to it.
• After just half a year as vice president, Garfield was assassinated and Arthur unexpectedly became the 21st President of the united states.
• To the surprise of reformers, Arthur took up the reform cause that had once led to his expulsion from office. He signed the Pendleton Act into law, and enforced its provisions vigorously.
• Suffering from poor health, Arthur made only a limited effort to secure renomination in 1884; he retired at the close of his term. As journalist Alexander McClure would later write, “No man ever entered the Presidency so profoundly and widely distrusted as Chester Alan Arthur, and no one ever retired … more generally respected, alike by political friend and foe.”

Chester A Arthur, 21st President of the United States of America

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• 21^st Amendment
• The Twenty-first Amendment to the United States Constitution repealed the Eighteenth Amendment, thereby ending Prohibition.

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• 21^st State
• Illinois – the ‘Land of Lincoln’ – was the 21st state to join the United States.
• Abraham Lincoln moved to Illinois when he was 21 and he met his future wife – Mary Todd – in Springfield when she was 21.
• Illinois currently has 21 electoral votes in the US Presidential Election.

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• Canada – Pier 21
• Pier 21 was, from 1928 to 1971, was the place where immigrants entered Canada. It was called the “Gateway to Canada.”

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• France – King Louis XVI
• 21 was a significant number in the life of French King Louis XVI
• On January 21, 1770, Louis XVI became engaged;
• On June 21, 1770, he got married;
• On January 21, 1782, he promulgated the suspension of a tax;
• On January 21, 1784 an enormous obelisk of snow was raised for him on the place Louis XV;
• On June 21, 1791,  Louis XVI was arrested;  and,
• On January 21, 1793, he goes up to the scaffold.
• Finally, the 5 letters of his first name added to XVI gives 21.

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• Japan-China
• The Twenty-One Demands were a set of demands which were sent to the Chinese government by the Japanese government of Okuma Shigenobu in 1915.

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• Poland
• The 21 Demands of MKS led to the foundation of Solidarity in Poland.

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In folklore, legends and mythology

• The Mayan Calendar
• December 21^st 2012, according to some interpretations of the Mayan calendar was the predicted date of an apocalyptic event: ‘The planets are aligned the sun will activate, let the deluge come’.
• It turned out to be bollocks though (see also this post)

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• Ghost Ship 21
• A ghost ship, also known as a phantom ship, is a ship with no living crew aboard. It may be a ghostly vessel in folklore or fiction, such as the Flying Dutchman, or a real derelict found adrift with its crew missing or dead, like the Mary Celeste. The term is sometimes also used for ships that have been decommissioned but not yet scrapped.
• There have been many examples throughout history, for example,
• Undated: The Caleuche is a mythical ghost ship which, according to local folklore and Chilota mythology, sails the seas around Chiloé Island, Chile, at night.
• 1738 onwards: The Palatine Light, a ship who lost half her crew running aground off Rhode Island, possibly being lured there and pillaged by the locals. Said to appear every December.
• 1748 onwards: The Lady Lovibond is said to have been deliberately wrecked on Goodwin Sands on 13 February and to reappear off the Kent coast every fifty years.
• 1786 onwards: The Ghost Ship of Northumberland Strait, a burning ship seen regularly between Prince Edward Island and New Brunswick.
• 1795 onwards: The Flying Dutchman, a ship manned by a captain condemned to eternally sail the seas, has long been the principal ghost ship legend among mariners and has inspired several works.
• 1813 onwards: After the American schooner Young Teazer was sunk in an explosion during the War of 1812, a burning apparition known as the “Teazer Light” has been reported off Maine.
• 1858 onwards: The Eliza Battle, a paddle steamer that burned in 1858 on the Tombigbee River in Alabama, is purported to reappear, fully aflame, on cold and windy winter nights to foretell of impending disaster.
• 1878 onwards: An apparition has been reported where the HMS Eurydice sank off the Isle of Wight. Witnesses include a Royal Navy submarine in the 1930s and Prince Edward, Earl of Wessex, in 1998.
• 1872 or 1882: The Iron Mountain riverboat, according to legend, mysteriously disappeared while travelling the Mississippi River and left the barges it was towing adrift. In reality, the ship sank in 1882 near Vicksburg after running aground, and its fate was never mysterious.
• 1928: The København was last heard from on December 28, 1928. For two years following its disappearance sightings of a mysterious five-masted ship fitting its description were reported in the Pacific Ocean.
• Historically attested
• 1855: HMS Resolute was discovered drifting off the coast of Baffin Island. It had been one of four vessels from Edward Belcher’s search expedition for John Franklin that had been abandoned the previous year when it was trapped in pack ice in Viscount Melville Sound. The ship drifted some 1,200 miles (1,900 km) before it was found, freed from the ice.
• 1872: Amazon (later renamed Mary Celeste). In 1872 the Mary Celeste, perhaps the most historically famous derelict, was found abandoned between mainland Portugal and the Azores archipelago. It was devoid of all crew, but largely intact and under sail, heading toward the Strait of Gibraltar. While Arthur Conan Doyle’s story “J. Habakuk Jephson’s Statement” based on this ship added some strange phenomena to the tale (such as that the tea found in the mess hall was still hot), the fact remained that the last log entry was 11 days prior to the discovery of the ship.
• 1884: In 1884 the Resolven was found abandoned between Baccalieu Island and Catalina, Newfoundland and Labrador, with its lifeboat missing. Other than a broken yard, it had suffered minimal damage. A large iceberg was sighted nearby. It has been claimed that none of the seven crew members or four passengers were accustomed to northern waters and it was suggested that they panicked when the ship was damaged by ice,[9] launched the lifeboat, and swamped, though no bodies were found. Three years later, Resolven was wrecked while returning to Newfoundland from Nova Scotia with a load of lumber.
• 1917: Zebrina, a sailing barge, departed Falmouth, England, with a cargo of Swansea coal bound for Saint-Brieuc, France. Two days later she was discovered aground on Rozel Point, south of Cherbourg, without damage except for some disarrangement of her rigging, but with her crew missing.
• 1921: The Carroll A. Deering, a five-masted cargo schooner, was found stranded on a beach on Diamond Shoals, North Carolina. The ship’s final voyage had been the subject of much debate and controversy, and was investigated by six departments of the US government, largely because it was one of dozens of ships that sank or went missing within a relatively short period of time. While paranormal explanations have been advanced, the theories of mutiny or piracy are considered more likely.
• 1931: The Baychimo was abandoned in the Arctic Ocean when it became trapped in pack ice and was thought doomed to sink, but remained afloat and was sighted numerous times over the next 38 years without ever being salvaged.
• 1933: A lifeboat from the 1906 wreck of the passenger steamship SS Valencia off the southwest coast of Vancouver Island was found floating in the area in remarkably good condition 27 years after the sinking. Sailors have also reported seeing the ship itself in the area in the years following the sinking, often as an apparition that followed down the coast.
• 1955: The MV Joyita was discovered abandoned in the Pacific. A subsequent inquiry found the vessel was in a poor state of repair, but determined the fate of passengers and crew to be “inexplicable on the evidence submitted at the inquiry”.
• 1959: A ghost submarine was found floating without a crew in the Bay of Biscay off northern Spain. It was later discovered that the empty sub was being towed by another vessel and the chain had snapped.
• 1969: The Teignmouth Electron was found adrift and unoccupied in the Atlantic Ocean. Investigation led to the conclusion that its sole crewmember, Donald Crowhurst, had suffered a psychiatric breakdown while competing in a solo around-the-world race and committed suicide by jumping overboard.
• 2003: The High Aim 6 was found drifting in Australian waters, 80 nautical miles (150 km; 92 mi) east of Rowley Shoals, with its crew missing. The derelict was subsequently scuttled.
• 2006: The tanker Jian Seng was found off the coast of Weipa, Queensland Australia in March. Its origin or owner could not be determined, and its engines had been inoperable for some time.
• 2006: In August the “Bel Amica” was discovered off the coast of Sardinia. The Coast Guard crew that discovered the ship found half eaten Egyptian meals, French maps of North African seas, and a flag of Luxembourg on board.
• 2007: A 12-metre catamaran, the Kaz II, was discovered unmanned off the coast of Queensland, northeast Australia in April.[18] The yacht, which had left Airlie Beach on Sunday 15 April, was spotted about 80 nautical miles (150 km) off Townsville, near the outer Great Barrier Reef on the following Wednesday. When boarded on Friday, the engine was running, a laptop was running, the radio and GPS were working and a meal was set to eat, but the three-man crew were not on board. All the sails were up but one was badly shredded, while three life jackets and survival equipment, including an emergency beacon, were found on board. A search for the crew was abandoned on Sunday 22nd as it was considered unlikely that anyone could have survived for that period of time.
• 2008: The abandoned 50 ton Taiwanese fishing vessel Tai Ching 21 was found drifting near Kiribati on 9 November. The ship had suffered a fire several days previously, and its lifeboat and three life rafts were missing. No mayday call was received, and the ship had last been heard from on 28 October. A search of 21,000 square miles (54,000 square km) of the Pacific Ocean north of Fiji by a US Air Force C-130 Hercules and a New Zealand Air Force P-3 Orion found no trace of the Taiwanese captain or crew (18 Chinese, 6 Indonesians, and 4 Filipinos).
• 2012: The Ryou-Un Maru, a Japanese fishing vessel swept away by the March 2011 tsunami, was found floating adrift towards Canada after nearly a year at sea, no crew believed to be on board. The vessel was sunk on April 5, 2012 by the United States Coast Guard.

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In sports

• The jersey number 21 has been retired by several North American sports teams in honor of past playing greats or other key figures:
• In Major League Baseball: the Cleveland Indians, for Hall of Famer Bob Lemon, the Milwaukee Braves, for Hall of Famer Warren Spahn (the number continues to be honored by the team in its current home of Atlanta);  the Pittsburgh Pirates, for Hall of Famer Roberto Clemente (following his death in a plane crash while attempting to deliver humanitarian aid to victims of an earthquake in Nicaragua);

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• In the NBA: the Atlanta Hawks, for Hall of Famer Dominique Wilkins; the Boston Celtics, for Hall of Famer Bill Sharman; the Detroit Pistons, for Hall of Famer Dave Bing; the Sacramento Kings, for Vlade Divac; the Minnesota Timberwolves have not retired the number, but have not issued it since Kevin Garnett was traded from the team in 2007.

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• In the NHL: the Chicago Blackhawks, for Hall of Famer Stan Mikita; the Colorado Avalanche, for likely future Hall of Famer Peter Forsberg; the Pittsburgh Penguins, for Michel Brière; the Toronto Maple Leafs have a policy of not retiring numbers unless the player honored either died or suffered a career-ending incident while a member of the team. Other players whose numbers would otherwise be retired instead have their numbers enshrined by the team as “Honored Numbers”, which remain in circulation for future players. The number 21 is currently honored for Hall of Famer Börje Salming.

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• No NFL team has retired the number 21.

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• In basketball: 21 is a variation of street basketball, in which each player, of which there can be any number, plays for himself only (i.e. not part of a team); the name comes from the requisite number of baskets.
• In 3×3, a formalized version of three-on-three half-court basketball, the game ends by rule once either team has scored 21 points in regulation. Scoring is significantly different from traditional basketball rules, with free throws and baskets made from inside the three-point arc worth 1 point, and baskets made from outside the arc worth 2 points.
• In badminton, and table tennis (before 2001), 21 points are required to win a game.
• Eyeshield 21 is a Japanese anime about football.
• In the NASCAR Sprint Cup Series the number 21 has long been the car number for Wood Brothers Racing

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In books, music, tv and movies

• 21 is the sophomore album from British singer-songwriter Adele, recently acclaimed for her title song for the Bond movie Skyfall.
• Century 21 Television (producers of Sylvia and Gerry Anderson Supermarionation shows like Thunderbirds and Captain Scarlet and the Mysterons).
• Cinema 21 is an independently-owned movie theatre in Portland, Oregon featuring art house films. Cinema 21, 616 NW 21st Avenue, Portland, Oregon 97209 USA
• Cinema 21, is also the name of the largest cinema chain in Indonesia, established in the entertainment industry in 1987.
• “21” is the fact-based story about six MIT students who were trained to become experts in card counting and subsequently took Vegas casinos for millions in winnings.
• Wedding In Las Vegas is a docu-drama about a group of students who, using a wedding as a cover story, also defeat the casino’s Blackjack tables using card counting techniques.

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In militaria

• Mig-21
• The Mikoyan-Gurevich MiG-21 is a supersonic jet fighter aircraft, designed by the Mikoyan-Gurevich Design Bureau in the Soviet Union. It was popularly nicknamed “balalaika”, from the aircraft’s planform-view resemblance to the Russian stringed musical instrument or olówek (English: pencil) by Polish pilots due to the shape of its fuselage.
• Early versions are considered second-generation jet fighters, while later versions are considered to be third-generation jet fighters.
• Some 50 countries over four continents have flown the MiG-21, and it still serves many nations a half-century after its maiden flight. The fighter made aviation records. At least by name, it is the most-produced supersonic jet aircraft in aviation history and the most-produced combat aircraft since the Korean War, and it had the longest production run of a combat aircraft (1959 to 1985 over all variants).

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• IAI Kfir F-21
• The Israel Aircraft Industries Kfir F-21 is an Israeli-built all-weather, multirole combat aircraft based on a modified French Dassault Mirage 5 airframe, with Israeli avionics and an Israeli-made version of the General Electric J79 turbojet engine.
• The Kfir entered service with the IAF in 1975, the first units being assigned to the 101st “First Fighter” Squadron. Over the following years, several other squadrons were also equipped with the new aircraft. The role of the Kfir as the IAF’s primary air superiority asset was short-lived, as the first F-15 Eagle fighters from the United States were delivered to Israel in 1976.
• The Kfir’s first recorded combat action took place on November 9, 1977, during an Israeli air strike on a training camp at Tel Azia, in Lebanon. The only air victory claimed by a Kfir during its service with the IAF occurred on June 27, 1979 when a Kfir C.2 shot down a Syrian MiG-21.
• Twenty-five modified Kfir C.1s were leased to the US Navy and the US Marine Corps from 1985 to 1989, to act as adversary aircraft in dissimilar air combat training (DACT). These aircraft, designated F-21A Kfir, had narrow-span canard foreplanes and a single small rectangular strake on either side of the nose which considerably improved the aircraft’s maneuverability and handling at low speeds.

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• Blücher 21 cm/45 (8.27″) SK L/45
• Used afloat only on the Armored Cruiser Blücher which was sunk at the World War I battle of Dogger Bank.  After her sinking, four reserve guns were given to the German Army.
• During World War II these guns were used as coastal artillery.  They were then supplied with a better ballistically shaped shell and with a larger propellant charge for increased range.
• Constructed of a tube, two layers of hoops and a jacket.  Used the Krupp horizontal sliding wedge breech block.  About 16 guns were made.

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• 21-K
• The 45 mm anti-aircraft gun (21-K) was a Soviet design adapted from the 45 mm anti-tank gun M1937 (53-K). This was a copy of a 3.7 cm (1.5 in) German weapon designed by Rheinmetall that was sold to the Soviets before Hitler came to power in 1933 that had been enlarged to 45 mm (1.8 in) in increase its penetrating power.
• It was used by the Soviet Navy to equip almost all of their ships from 1934 as its primary light anti-aircraft gun until replaced by the fully automatic 37 mm 70-K gun from 1942 to 1943.
• It was used in World War II and during the Cold War as the Soviets exported their World War II-era ships to their friends and allies.
• However it was not very effective as its slow rate of fire and lack of a time fuze required a direct hit to damage targets.

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• GAU-21 (M3M)
• The M3M was designated by the U.S. Navy as the GAU-21 in 2004 and is currently used by all services within the U.S. Department of Defense (DoD).
• An evolution of the M3 .50-caliber heavy machine gun, it produces a blistering 1,100 rounds per minute cyclic rate of fire through the use of open-bolt operation and a dual recoil buffer system. Operating independent of either electrical or hydraulic power sources, the M3M/GAU-21’s unique soft mount system enhances weapon accuracy and minimizes the firing vibration transmitted to the airframe.
• FN Herstal has been awarded a solesource U.S. Navy contract to produce the M3M .50 caliber machine guns under the Gun, Aircraft, Unit-21 (GAU-21) designation for Navy and Marine Corps rotary-wing assault aircraft.
• The FN GAU-21 (M3M) is a .50 caliber (12.7x99mm) single barrel rapid-fire machine gun suitable for rotary-wing aircraft applications providing defensive firepower ranging out to nearly 2000 meters.

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• BRNO 21
• BRNO is neither German nor Austrian (although it was once located in the Austro-Hungarian Empire), but they produced the BRNO model designation 21 and 22 as post-War sporting rifles.

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• GLOCK 21
• Almpst an American icon, the Glock 21 is a .45 caliber pistol. Countless law enforcement units swear by this superior pistol for more than just its above-average magazine capacity of 13 rounds.

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• SIG SAUER® P210®
• The SIG SAUER® P210®, the timeless pistol of the Swiss Army, is once again in production by SIG SAUER GmbH in Germany. This historic gun features the same precision and reliability as its ancestors, but also offers a number of modern improvements.
• The return of the SIG SAUER P210 Legend will now ensure that many more shooters will be able to enjoy one of the world’s most accurate and legendary firearms.

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• 21st Century Commander
• Internally, the 21st Century Commander is classic Colt. The stainless 4.25-inch barrel is rifled in the standard 1:16-inch left-hand twist. Each 21st Century Commander is serialized with a unique number that contains the letters “WC” for Wiley Clapp.

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• 21 Series Beretta
• The 21 Series Beretta pocket pistol (Bobcat) has the same dedication to advanced design, uncompromising quality and strict quality control that make the 92F, Cougar and Cheetah such international standouts.
• It has a user-friendly design, exclusive tip-up barrel allowing the user to easily load a round directly into the chamber or assisting in the safe clearing of the pistol by allowing a live round to be easily removed from the chamber and the bore quickly checked. Jamming and stovepiping problems are virtually eliminated by the open slide design shared by all small frame Berettas.
• Chambered for .22LR or .25ACP (6.35 mm), this compact, rugged small frame measures just 4.9 inches (125 mm) overall and weighs only 11.5 ounces (325 grams). It features a lightweight, alloy frame, blued steel slide, tip-up barrel, and double/single action. The Bobcat comes with a 7-round magazine for .22LR ammunition, or an 8 round magazine for .25 (6.35 mm)caliber cartridges.

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• Twenty-one Gun Salute
• Legend has it that Twenty-one guns are fired in U.S. national military salutes because the digits in 1776 add up to 21. However, despite the fact that the year 1776 is deeply significant to Americans and the total of its digits does add up to 21, the legend is untrue because the custom of the 21-gun salute antedates the American Revolution by at least several decades.
• Also interesting is the fact that, although we now view weaponry salutes as honors proudly bestowed by fighting men upon those of high rank or great achievement, saluting in days long ago was an act of submission; a tangible way of demonstrating that the one performing the action was voluntarily placing himself in the power of the one being saluted. Guns would be emptied a ritual number of times, or sails would be lowered, or spears would be pointed towards the ground, the significance being that those carrying out the act were saying “I yield to your authority, and as proof I’ve just rendered my weapon incapable of being used against you.”
• Over time the practice evolved into a custom honorary and ceremonial as well as practical. Today’s salute is far more a mark of respect than an act of submission.
• Cannons became part of weaponry salutes in the 14th century.  A just-emptied cannon was a useless piece of ordnance and so made a fine visible display of the lack of hostile intent. Warships took to firing honorary seven-gun salutes, with that number likely chosen for its astrological and biblical significance. Because those crewing cannons on land had access to far greater supplies of powder, they were able to fire three guns (a number chosen for its mystical significance) for every shot fired afloat, making the honorary salute by shore batteries 21 guns.
• Eventually, an understanding was reached that the international salute should be established as 21 guns.
• Today, the national salute of 21 guns is fired in honor of a national flag, the sovereign or chief of state of a foreign nation, a member of a reigning royal family, and the President, ex-President, and President-elect of the United States. It is also fired at noon of the day of the funeral of a President, ex-President, or President-elect; Washington’s Birthday; Presidents’ Day; and the Fourth of July. On Memorial Day, a salute of 21 minute guns (i.e., guns discharged at one-minute intervals) is fired at noon while the flag is flown at half staff.

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In other stuff

• We are currently living in the 21^st Century, which spans the years from 2001 to 2100;
• There are 21 letters in the Italian alphabet;
• 21 is the number representing the maturity and the responsibility for an individual;
• In most USA states 21 is the drinking age;
• In some countries 21 is the voting age;
• Cities on latitude 21 North include:  Aguascalientes, Cancún, and León, in Mexico; Jeddah, and Mecca in Saudi Arabia; Honolulu, Hawaii; Nagpur, Maharashtra, India; and Hanoi, Vietnam.
• Cities on latitude 21 South include: Francistown, Botswana; and Nuku’Alofa, Tonga.
• Cities on longitude 21 West include: Reykjavík, Iceland.
• Cities on longitude 21 East include: Warsaw, Poland; Pristina, Kosovo; and Skopje, Macedonia.21 is a card game, also called vingt-et-un (French for “twenty-one”), pontoon, or blackjack;
• Twenty One, was the name of a TV quiz show that ran from 1956 to 1958, most remembered for the scandal that the wins were fixed – it was remade in 2000;
• There are 21 spots on a standard cubical (six-sided) die (1+2+3+4+5+6);
• There are 21 trump cards of the tarot deck if one does not consider The Fool to be a proper trump card;
• In Israel, the number is associated with the profile 21 (the military profile designation granting an exemption from the military service);
• 21 grams is the weight of the soul, according to research by Duncan MacDougall;
• 21 is the designation of a US Highway connecting Wytheville, Virginia and Beaufort, South Carolina, a truncation of a route that once connected Cleveland, Ohio and Jacksonville, Florida, among other highways past and present;
• 21 is the number of the French department Côte-d’Or;
• In France XXI is a journal devoted to long-form journalism;
• ’21’ is a landmark New York restaurant perfectly positioned in midtown Manhattan;
• Forever 21 is an American chain of clothing retailers with branches in major cities in the Americas, Europe, Asia, and the Middle East that offers trendy clothing and accessories for young women, men, and girls at low, affordable prices.

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