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

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).

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).