73 (number) - in Mathematics

In Mathematics

• Seventy-three is the 21st prime number. The previous is seventy-one, with which it comprises the 8th twin prime. It is also a permutable prime with thirty-seven. 73 is a star number.
• 73 is the largest minimal Primitive root in the first 100000 primes. In other words, if p is one of the first 100000 primes, then at least one of the primes 3, 5, 7, 11, 13, 17, ..., 73 is a primitive root modulo p.
• 73 is the smallest prime congruent to 1 modulo 24.
• 73 is an emirp.
• The mirror of 73, the 21st prime number, 37, is the 12th prime number. The number 21 includes factors 7 and 3. The number 21 in binary is 10101 and Seventy-three in binary, 1001001, both are a palindrome. 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.
• The square root of 73 is approximately 8.544. The sum of which (8+5+4+4) equals the product of 7 and 3; 21.
• Every positive integer can be written as the sum of 73 or fewer sixth powers (see Waring's problem).
• In base 5, the smallest prime with a composite sum of digits is 73.
• 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).