Levy's Conjecture

Levy (1963) noted that

			(1)
			(2)

and from this observation, conjectured that all odd numbers  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  (Corbit 1999).

The number of ways  to express  as  for  and  primes and , 2, ... are 0, 0, 0, 1, 2, 2, 2, 2, 4, 2, 3, 3, 3, 4, 4, ... (OEIS A046927).

REFERENCES:

Corbit, D. "Conjecture on Odd Numbers." sci.math posting. Nov 19, 1999. https://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."