In number theory, Lemoine's conjecture, named after Émile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.
To put it algebraically, 2n + 1 = p + 2q always has a solution in primes p and q (not necessarily distinct) for n > 2. The Lemoine conjecture is similar to but stronger than Goldbach's weak conjecture.
- Emile Lemoine, L'intermédiare des mathématiciens, 1 (1894), 179; ibid 3 (1896), 151.
- H. Levy, "On Goldbach's Conjecture", Math. Gaz. 47 (1963): 274
- L. Hodges, "A lesser-known Goldbach conjecture", Math. Mag., 66 (1993): 45–47. doi:10.2307/2690477. JSTOR 2690477
- John O. Kiltinen and Peter B. Young, "Goldbach, Lemoine, and a Know/Don't Know Problem", Mathematics Magazine, 58(4) (Sep., 1985), pp. 195–203. doi:10.2307/2689513. JSTOR 2689513
- Richard K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: C1