73 (number)

73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

← 72 73 74 →
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Cardinal	seventy-three
Ordinal	73rd (seventy-third)
Factorization	prime
Prime	21st
Divisors	1, 73
Greek numeral	ΟΓ´
Roman numeral	LXXIII
Binary	10010012
Ternary	22013
Octal	1118
Duodecimal	6112
Hexadecimal	4916

In mathematics

73 is:

• the 21st prime number. The previous is 71, with which it composes the 8th twin prime.
• a permutable prime with 37.
• a star number.[1]
• the largest minimal primitive root in the first 100,000 primes. In other words, if p is one of the first 100,000 primes, then at least one of the numbers 2, 3, 4, 5, 6, ..., 72, 73 is a primitive root modulo p.
• the smallest prime congruent to 1 modulo 24.
• an emirp, meaning that the reverse of 73, that is, 37, is also a prime number.[2] 73 is the 21st prime number while 37 is the 12th prime number.
• has the product property[3] (i.e., the product of its base-10 digits is precisely its index in the sequence of primes: 7 × 3 = 21 and 73 is the 21st prime number). It also has the mirror property[3] (i.e., its permutable prime 37 is the 12th prime number, which is, again, the reverse of 21). Because of these two properties, it is the sole Sheldon prime,[4] an homage to Sheldon Cooper, the fictional theoretical physicist on the television show The Big Bang Theory who claimed that 73 is the best number.
• the smallest prime with a composite sum of digits, in base 5.
• palindromic in bases 2 (1001001₂) and 8 (111₈).
• the only prime repunit in base 8 (111₈).
• the smallest factor of the first composite generalized Fermat number in base 10 (10⁴ + 1 = 10,001 = 73 × 137).

Also:

• The number 21 has prime factors 7 and 3. The number 21 in binary is 10101; 7 in binary is 111, 3 in binary is 11, and seventy-three in binary is 1001001. All of these are palindromes. In addition, of the 7 binary digits representing 73, there are 3 ones. Also, 37 + 12 = 49 (seven squared) and 73 + 21 = 94 = 47 × 2, 47 + 2 also being equal to seven squared. Additionally, both 73 and its mirror, 37, are sexy primes twice over, as 31, 43, 67 and 79 are all prime numbers.
• In addition to having prime factors 7 and 3, the number 21 represents the ternary (base-3) equivalent of the decimal numeral 7, or 21₃ = 7₁₀.
• 7³ = 343, a palindrome. Replacing the first two digits of 343 with their sum yields 73.
• Every positive integer can be written as the sum of 73 or fewer sixth powers (see Waring's problem).

In science

• The atomic number of tantalum

In astronomy

• Messier object M73, a magnitude 9.0 apparent open cluster in the constellation Aquarius.
• The New General Catalogue object NGC 73, a barred spiral galaxy in the constellation Cetus.
• The number of seconds it took for the Space Shuttle Challenger OV-099 shuttle to explode after launch.
• 73 is the number of rows in the 1,679-bit Arecibo message, sent to space in search for extraterrestrial intelligence.

In other fields

73 is also:

• The number of days in 1/5 of a non-leap year.
• The year AD 73, 73 BC, or 1973.
• The number of books in the Catholic Bible.[5]
• Amateur radio operators and other morse code users commonly use the number 73 as a "92 Code" abbreviation for "best regards", typically when ending a QSO (a conversation with another operator). These codes also facilitate communication between operators who may not be native English speakers. In Morse code, 73 is an easily recognized palindrome: ( - - · · · · · · - - ).
• 73 (also known as 73 Amateur Radio Today) was an amateur radio magazine published from 1960 to 2003.
• 73 was the number on the Torpedo Patrol (PT) boat in the TV show McHale's Navy.
• The registry of the U.S. Navy's nuclear aircraft carrier USS George Washington (CVN-73), named after U.S. President George Washington.
• No. 73 was the name of a 1980s children's television programme in the United Kingdom. It ran from 1982–1988 and starred Sandi Toksvig.
• Pizza 73 is a Canadian pizza chain.
• Game show Match Game '73 in 1973.
• Fender Rhodes Stage 73 Piano.
• Sonnet 73 by William Shakespeare.
• The number of the French department Savoie.
• On a CB radio, 10-73 means "speed trap at..."

In sports

• In international curling competitions, each side is given 73 minutes to complete all of its throws.
• In baseball, the single-season home run record set by Barry Bonds in 2001.
• In basketball, the number of games the Golden State Warriors won in the 2015-16 season (73-9), the most wins in NBA history.
• NFL: In the 1940 NFL championship game, the Bears beat the Redskins 73–0, the largest score ever in an NFL game. (The Redskins won their previous regular season game, 7–3).

See also

• List of highways numbered 73

References

1. "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers: 6*n*(n-1) + 1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
2. "Sloane's A006567 : Emirps". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
3. Byrnes, Jessie; Spicer, Chris; Turnquist, Alyssa (November 2015). "The Sheldon Conjecture". Math Horizons. 23 (2): 12–15. doi:10.4169/mathhorizons.23.2.12. ISSN 1072-4117.
4. Pomerance, Carl; Spicer, Chris (April 2019). "Proof of the Sheldon conjecture" (PDF). Amer. Math. Monthly. to appear.
5. "Catholic Bible 101". Catholic Bible 101. Retrieved 16 September 2018.