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ya, I read that he wasnt overly concerned about true primality. Interesting link you provided though. I had never even thought of just comparing the quotient to the factor, simple and effective, I...

Im not up on nasm either but I think Eri523 hit it right on the head, it looks like youre creating a single dword value instead of an array which means your:

mov DWORD[primes + ESI * 4], EAX
...