Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that there are infinitely many twin primes (Ball and Coxeter 1987). The conjecture has never been proven true or refuted.
de Polignac's Conjecture
See also
Even Number, Goldbach Conjecture, Levy's Conjecture, Twin PrimesExplore with Wolfram|Alpha
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 64, 1987.Burton, D. M. Elementary Number Theory, 4th ed. Boston, MA: Allyn and Bacon, p. 76, 1989.de Polignac, A. "Six propositions arithmologiques déduites de crible d'Ératosthène." Nouv. Ann. Math. 8, 423-429, 1849.de Polignac, A. Comptes Rendus Paris 29, 400 and 738-739, 1849.Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Dover, 2005.Cite this as:
Weisstein, Eric W. "de Polignac's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/dePolignacsConjecture.html