
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Twin primes are pairs of primes which differ by two. (This name was coined by Stäckel in 1916.) The first twin primes are {3,5}, {5,7}, {11,13,} and {17,19}. It has been conjectured that there are infinitely many twin primes (see the twin prime conjecture for further information). Using sieve techniques, it has been proven that the sum of the reciprocals of the twin primes converge (see Brun's constant). It is trivial to show that other than the first pair, all pairs of twin primes have the form {6n1, 6n+1}. It takes more work to prove this variant of Wilson's theorem:
See the other entries and pages linked below for more technical information.
See Also: TwinPrimeConstant, BrunsConstant, PrimeKtupleConjecture Related pages (outside of this work)
References:
Chris K. Caldwell © 19992019 (all rights reserved)
