32. The Number 73

I don’t Know why I thought of this but I did.

Sheldon Cooper

(yes the fictional character from the big bang theory)

believes the number 73 is the best number..

**this has been copied and pasted from wiki…  

• 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 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.

• 73 is the smallest prime congruent to 1 modulo 24.

• 73 is an emirp, meaning that the reverse of 73, that is, 37, is also a prime number. 73 is also the 21st prime number while 37 is the 12th prime number.

• The number 21 includes 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.

• 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).

For more…

http://en.wikipedia.org/wiki/73_(number)