Andrica’s conjecture

Conjecture (Dorin Andrica). Given the nth prime pn, it is always the case that 1>pn+1-pn.

This conjecture remains unproven as of 2007. The conjecture has been checked up to n=105 by computers.

The largest known difference of square roots of consecutive primes happens for the small n=4, being approximately 0.67087347929081. The difference of the square roots of the primes 10314-1929 and 10314+2318 (which cap a prime gap of 4247 consecutive composite numbersMathworldPlanetmath discovered in 1992 by Baugh & O’Hara) is a very small number which is obviously much smaller than 1.


  • 1 D. Baugh & F. O’Hara, “Large Prime Gaps” J. Recr. Math. 24 (1992): 186 - 187.
Title Andrica’s conjecture
Canonical name AndricasConjecture
Date of creation 2013-03-22 16:41:22
Last modified on 2013-03-22 16:41:22
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 8
Author PrimeFan (13766)
Entry type Conjecture
Classification msc 11A41
Synonym Andrica conjectureMathworldPlanetmath