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Mersenne prime

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1: 27.18 Methods of Computation: Primes
For small values of n , primality is proven by showing that n is not divisible by any prime not exceeding n . …
2: 27.12 Asymptotic Formulas: Primes
where λ ( α ) depends only on α , and ϕ ( m ) is the Euler totient function (§27.2). A Mersenne prime is a prime of the form 2 p 1 . The largest known prime (2018) is the Mersenne prime 2 82 , 589 , 933 1 . For current records see The Great Internet Mersenne Prime Search. …
3: 27.22 Software
  • GIMPS. This includes updates of the largest known Mersenne prime.

  • 4: Bibliography G
  • GIMPS (website)
  • 5: Errata
  • Paragraph Prime Number Theorem (in §27.12)

    The largest known prime, which is a Mersenne prime, was updated from 2 43 , 112 , 609 1 (2009) to 2 82 , 589 , 933 1 (2018).