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).

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."