It is well known fact that it is very hard to prove Goldbach's strong conjecture but perhaps some weaker variations can be proved(or disproved) ,so my question is: Is it true that every even number greater than 10 can be represented as the sum of an odd prime number and an odd semiprime?
Some counterexamples: 12, 14, 16, 30. My perl program can't find any more smaller than 100000.
EDIT: I didn't know that semiprimes are defined to include squares. When I comment out the line that filters them, nothing is output up to 100000. I'll leave this answer here as an example of wrongness.