prime pairs | prime twins

Twin primes are pairs of primes of the form (p, p + 2). The term "twin prime" was coined by Paul Stäckel (1862-1919; Tietze 1965, p. 19). The first few twin primes are n ± 1 for n = 4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150, 180, 192, 198, 228, 240, 270, 282, ... (OEIS A014574). Explicitly, these are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), ... (OEIS A001359 and A006512). All twin primes except (3, 5) are of the form 6n ± 1. It is conjectured that there are an infinite number of twin primes (this is one form of the twin prime conjecture), but proving this remains one of the most elusive open problems in number theory.

bitwin chain | Brun's constant | cousin primes | de Polignac's conjecture | prime arithmetic progression | prime constellation | prime gaps | sexy primes | twin composites | twin prime cluster | twin prime conjecture | twin primes constant