Fast Constructive Recognition of a Black Box Group Isomorphic to Sn or An using Goldbach's Conjecture

摘要

The well-known Goldbach Conjecture (GC) states that any sufficiently large even num- ber can be represented as a sum of two odd primes. Although not yet demonstrated, it has been checked for integers up to 10~14. Using two stronger versions of the conjecutre, we offer a simple and fast method for recognition of a gray box group G known to be isomor- phic to Sn(or An) with known n≥20, i.e. for construction of an isomorphism from G to Sn (or An).