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 is a consequence of Fermat's theorem on sums of two squares, which states that an odd prime formula_20 is expressible as the sum of two squares, formula_187, and therefore factorizable as formula_188, exactly when formula_20 is 1 mod 4. Not every ring is a unique factorization domain. For instance, in the ring of numbers formula_190 (for integers formula_34 and formula_35) the number formula_193 has two factorizations formula_194, where neither of the four factors can be reduced any further, so it does not have a unique factorization. In order to extend unique factorization to a larger class of rings, the notion