Pairs of primes of the form (p, p + 4) are called cousin primes. The first few are (3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), ... (OEIS A023200 and A046132). A large pair of cousin (proven) primes start with p = {9771919142·[(53238·7879#)^2 - 1] + 2310}·53238·7879#/385 + 1, where 7879# is a primorial. These primes have 10154 digits and were found by T. Alm, M. Fleuren, and J. K. Andersen. As of Jan. 2006, the largest known pair of cousin (probable) primes are 630062·2^37555 + 3, 7, which have 11311 digits and were found by D. Johnson in May 2004.

Brun's constant | prime constellation | sexy primes | twin primes | twin primes constant