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Williams number

In Williams number's article, we will explore a series of perspectives and reflections on this topic that has captured the attention of many. From its origin to its current implications, we will delve into its relevance in today's world and how it has impacted different aspects of society. Through detailed analysis and expert opinions, we will present a broad and complete vision of Williams number, with the aim of understanding its importance and influence in various spheres of daily life.

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Not to be confused with Newman–Shanks–Williams prime.

In number theory, a Williams number base b is a natural number of the form for integers b ≥ 2 and n ≥ 1.[1] The Williams numbers base 2 are exactly the Mersenne numbers.

A Williams prime is a Williams number that is prime. They were considered by Hugh C. Williams.[2]

It is conjectured that for every b ≥ 2, there are infinitely many Williams primes for base b.

See also

References

  1. ^ Williams primes
  2. ^ See Table 1 in the last page of the paper: Williams, H. C. (1981). "The primality of certain integers of the form 2 A rn – 1". Acta Arith. 39: 7–17. doi:10.4064/aa-39-1-7-17.


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