Levy's conjecture

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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 10⁹.

The conjecture was posed by Émile Lemoine in 1895, but in more recent years came to be attributed to Hyman Levy who pondered it in the 1960s.

[edit] References

• Eric W. Weisstein, Levy's Conjecture at MathWorld.
• Richard K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: C1
• L. Hodges, "A lesser-known Goldbach conjecture", Math. Mag., 66 (1993): 45 - 47.
• H. Levy, "On Goldbach's Conjecture", Math. Gaz. 47 (1963): 274

[edit] External links

• Levy's Conjecture by Jay Warendorff, The Wolfram Demonstrations Project.