In number theory, Levy's conjecture 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 Levy conjecture is similar to but stronger than Goldbach's weak conjecture.
For example, 47 = 13 + 2 × 17 = 37 + 2 × 5 = 41 + 2 × 3 = 43 + 2 × 2. (sequence A046927 in OEIS) counts how many different ways 2n + 1 can be represented as p + 2q.
According to MathWorld, the conjecture has been checked for all odd positive integers less than 10^9.
Reference:
http://en.wikipedia.org/wiki/Levy%27s_conjecture
