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From Wikipedia, the free encyclopedia

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.

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Transcription

Contents

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], 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 science

In astronomy

In other fields

73 is also:

In sports

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. ^ 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.
This page was last edited on 4 July 2019, at 10:22
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