twin prime constant
(another Prime Pages' Glossary entries)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

If we look at the number of twin primes less than x we see the usual irregularities associated with distributions of primes:

The number of twin primes less than x for x to 1,000

but back up and look again and the distribution looks much smoother:

The number of twin primes less than x for x to 100,000
(Click here for a graph to 1,000,000).

Hardy and Littlewood conjectured that there are about

2 C x/log(x)^2
twin primes less than or equal to x where the infinite product is the twin prime constant. See the page "a simple heuristic" linked below for information on how this conjecture is formed.

This constant was estimated by Wrench and others to be approximately 0.6601618158...

See Also: TwinPrime, BrunsConstant, PrimeKtupleConjecture

Related pages (outside of this work)

Chris K. Caldwell © 1999-2019 (all rights reserved)