Levy's Conjecture

Levy (1963) noted that


and from this observation, conjectured that all odd numbers >=7 are the sum of a prime plus twice a prime. This conjecture is a stronger version of the weak Goldbach conjecture and has been verified up to n<=10^9 (Corbit 1999).


The number of ways S(n) to express 2n+1 as p+2q for p and q primes and n=1, 2, ... are 0, 0, 0, 1, 2, 2, 2, 2, 4, 2, 3, 3, 3, 4, 4, ... (OEIS A046927).

See also

de Polignac's Conjecture, Goldbach Conjecture

Portions of this entry contributed by Daniel Dudley

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Corbit, D. "Conjecture on Odd Numbers." sci.math posting. Nov 19, 1999., L. "A Lesser-Known Goldbach Conjecture." Math. Mag. 66, 45-47, 1993.Levy, H. "On Goldbach's Conjecture." Math. Gaz. 47, 274, 1963.Sloane, N. J. A. Sequence A046927 in "The On-Line Encyclopedia of Integer Sequences."

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Levy's Conjecture

Cite this as:

Dudley, Daniel and Weisstein, Eric W. "Levy's Conjecture." From MathWorld--A Wolfram Web Resource.

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