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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?

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    http://www.math.utoledo.edu/~jevard/Page015.htm Has some references regarding improvements on Chen's theorem.2011-09-13

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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.

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    @Dan,12=3+9,9 is odd semiprime ;14=5+9 ;16=7+9; 30=5+25 ,25 is odd semiprime...so you are not right this time2011-09-13