Supersingular prime (moonshine theory) Supersingular prime (moonshine theory) In the mathematical branch of moonshine theory, a supersingular prime is a prime number that divides the order of the Monster group "M", which is the largest sporadic simple group. There are precisely fifteen supersingular prime numbers: the first eleven primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31), as well as 41, 47, 59, and 71. The non-supersingular primes are 37, 43, 53, 61, 67, and any prime number greater than or equal to 73. All supersingular primes are Chen primes, but 37, 53, and 67 are also Chen primes, and
Prime number a quadratic polynomial that (for integer arguments) is prime infinitely often. Euler's proof that there are infinitely many primes considers the sums of reciprocals of primes, Euler showed that, for any arbitrary real number formula_22, there exists a prime formula_20 for which this sum is bigger than formula_22. This shows that there are infinitely many primes, because if there were finitely many primes the sum would reach its maximum value at the biggest prime rather than growing past every formula_22. The growth rate of this sum is described more precisely by Mertens' second theorem. For comparison, the sum does not