twin prime conjecture
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

The (weak) twin prime conjecture is that there are infinitely many twin primes.

There is also a strong form of this conjecture [HL23] which states that there are about

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

See Also: BrunsConstant, TwinPrimeConstant

Related pages (outside of this work)


G. H. Hardy and J. E. Littlewood, "Some problems of `partitio numerorum' : III: on the expression of a number as a sum of primes," Acta Math., 44 (1923) 1-70.  Reprinted in "Collected Papers of G. H. Hardy," Vol. I, pp. 561-630, Clarendon Press, Oxford, 1966.

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