Largest known twin primes and sophie germain primes

摘要

The numbers 242206083 centre dot 2~(38880) +- 1 are twin primes. The number p = 2375063906985 centre dot 2~(19380) - 1 is a Sophie Germain prime, i.e. p and 2p + 1 are both primes. For p = 4610194180515 centre dot 2~(5056) - 1, the numbers p, p + 2 and 2p + 1 are all primes.