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Largest known twin primes and Sophie Germain primes
Authors:Karl-Heinz Indlekofer  Antal Já  rai
Institution:Universität GH Paderborn, FB 17, D-33095 Paderborn, Germany ; Universität GH Paderborn, FB 17, D-33095 Paderborn, Germany
Abstract:The numbers $242206083\cdot 2^{38880}\pm 1$ are twin primes. The number $p=2375063906985\cdot 2^{19380}-1$ is a Sophie Germain prime, i.e. $p$ and $2p+1$ are both primes. For $p=4610194180515\cdot 2^{5056}-1$, the numbers $p$, $p+2$ and $2p+1$ are all primes.

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