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Quasi-primes and the Goldbach conjecture

In 1742 Goldbach sent a letter to Euler which contained the conjecture that: Every even number greater than 2 is the sum of two prime numbers. It is easy to verify Goldbach's conjecture numerically up to some quite high limits but no proof has yet been found. I have long had the uneasy feeling that the conjecture is not about the prime numbers at all but would equally apply to any ‘sufficiently dense’ sequence of odd numbers. However a recent attempt to generalise the sieve of Eratosthenes has led me to regard Goldbach's conjecture with a good deal more respect.