Levy’s conjecture

Conjecture (Émile Lemoine). All odd integers greater than 5 can be represented as the sum of an odd prime and an even semiprime. In other words, 2n+1=p+2q always has a solution in primes p and q (not necessarily distinct) for n>2.

For example, 47=13+2×17=37+2×5=41+2×3=43+2×2. A046927 in Sloane’s OEIS counts how many different ways 2n+1 can be represented as p+2q.

The conjecture was first stated by Émile Lemoine in 1894. In 1963, Hyman Levy published a paper mentioning this conjecture in relationMathworldPlanetmath to Goldbach’s conjecture.


  • 1 L. E. Dickson, History of the Theory of Numbers Vol. I. Providence, Rhode Island: American Mathematical Society & Chelsea Publications (1999): 424
  • 2 R. K. Guy, Unsolved Problems in Number TheoryMathworldPlanetmathPlanetmath New York: Springer-Verlag 2004: C1
  • 3 L. Hodges, “A lesser-known Goldbach conjectureMathworldPlanetmath”, Math. Mag., 66 (1993): 45 - 47.
  • 4 É. Lemoine, “title” L’intermediaire des mathematiques 179 3 (1896): 151
  • 5 H. Levy, “On Goldbach’s Conjecture”, Math. Gaz. 47 (1963): 274
Title Levy’s conjecture
Canonical name LevysConjecture
Date of creation 2013-03-22 17:26:32
Last modified on 2013-03-22 17:26:32
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Conjecture
Classification msc 11P32
Synonym Levy conjectureMathworldPlanetmath
Synonym Lemoine’s conjecture