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Levy's Conjecture

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Levy's conjecture asserts that every odd number at least 7 is the sum of a prime and twice a prime. Levy (1963) noted that

13=3+(2×5)
(1)
19=5+(2×7),
(2)

and proposed this conjecture. It is a stronger version of the weak Goldbach conjecture and has been verified up to n<=10^9 (Corbit 1999).

LevysConjectureSolutions

The number of ways S(n) to express 2n+1 as p+2q for p and q primes and n=0, 1, ... 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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References

Corbit, D. "Conjecture on Odd Numbers." Nov. 19, 1999. https://groups.google.com/g/sci.math/c/HoCpH8gPDHM/m/gtU-fuSWnFMJ.Hodges, 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:

Weisstein, Eric W., with contributions by Daniel Dudley. "Levy's Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LevysConjecture.html

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