73 (number)

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
Quaternary 10214
Quinary 2435
Senary 2016
Octal 1118
Duodecimal 6112
Hexadecimal 4916
Vigesimal 3D20
Base 36 2136

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.

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 primes 3, 5, 7, 11, 13, 17, ..., 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.
  • the smallest prime with a composite sum of digits, in base 5.
  • palindromic in bases 2 (10010012) and 8 (1118).
  • 73 is the only prime repunit in base 8 (1118).
  • 73 is 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

In astronomy

In other fields

73 is also:

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

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. "Catholic Bible 101". Catholic Bible 101. Retrieved 16 September 2018.
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