balanced prime

If for the given nth prime pn the equality


is true, then pn is said to be a balanced prime. That is, the arithmetic meanMathworldPlanetmath of the given prime, the prime immediately below and the one immediately above, is equal to the middle prime. The first few are 5, 53, 157, 173, 211, 257, 263, 373, listed in A006562 of Sloane’s OEIS. As of 2006, the largest known balanced prime is 197418203×225000-1, discovered by David Broadhurst and François Morain using FastECPP and PrimeForm.

Title balanced prime
Canonical name BalancedPrime
Date of creation 2013-03-22 16:36:50
Last modified on 2013-03-22 16:36:50
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A41
Related topic StrongPrime
Related topic WeakPrime