TOPICS
Search

Levy's Conjecture


Levy (1963) noted that

13=3+(2×5)
(1)
19=5+(2×7),
(2)

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).

LevysConjectureSolutions

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

Explore with Wolfram|Alpha

References

Corbit, D. "Conjecture on Odd Numbers." sci.math posting. Nov 19, 1999. http://groups-beta.google.com/group/sci.math/msg/539c96e47e3ed582?hl=en&.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."

Referenced on Wolfram|Alpha

Levy's Conjecture

Cite this as:

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

Subject classifications