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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 →
Cardinalseventy-three
Ordinal73rd
(seventy-third)
Factorizationprime
Prime21st
Divisors1, 73
Greek numeralΟΓ´
Roman numeralLXXIII
Binary10010012
Ternary22013
Quaternary10214
Quinary2435
Senary2016
Octal1118
Duodecimal6112
Hexadecimal4916
Vigesimal3D20
Base 362136

Contents

In mathematicsEdit

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], as 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 scienceEdit

In astronomyEdit

In other fieldsEdit

73 is also:

In sportsEdit

  • 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 alsoEdit

ReferencesEdit

  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. ^ a b 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.