Every supersingular elliptic curve in characteristic p can be defined over the
prime subfieldFp.
The order of the Monster group is divisible by p.
The equivalence is due to
Andrew Ogg. More precisely, in 1975 Ogg showed that the primes satisfying the first condition are exactly the 15 supersingular primes listed above and shortly thereafter learned of the (then
conjectural) existence of a sporadic simple group having exactly these primes as prime divisors. This strange coincidence was the beginning of the theory of
monstrous moonshine.
All supersingular primes are
Chen primes, but 37, 53, and 67 are also Chen primes, and there are infinitely many Chen primes greater than 73.
Ogg, A. P. (1980). "Modular Functions". In Cooperstein, Bruce; Mason, Geoffrey (eds.). The Santa Cruz Conference on Finite Groups. Held at the University of California, Santa Cruz, Calif., June 25–July 20, 1979. Providence, RI: Amer. Math. Soc. pp. 521–532.
ISBN0-8218-1440-0.
MR0604631.