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 instance the Solovay–Strassen primality test on a given number formula_20 chooses a number formula_34 randomly from formula_42 to formula_210 and uses modular exponentiation to check whether formula_211 is divisible by formula_20. If so, it answers yes and otherwise it answers no. If formula_20 really is prime, it will always answer yes, but if formula_20 is composite then it answers yes with probability at most 1/2 and no with probability at least 1/2. If this test is repeated formula_1 times on the same number, the probability that a composite number could pass the test every time is at most formula_216. Because