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, $47=13+2\times 17=37+2\times 5=41+2\times 3=43+2\times 2$ . 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 relation to Goldbach’s conjecture.

References

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 Theory New York: Springer-Verlag 2004: C1
3 L. Hodges, “A lesser-known Goldbach conjecture”, 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 conjecture
Synonym	Lemoine’s conjecture