Thread: Prime gaps
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May25-08, 06:13 AM
P: 32
Is Goldbach's conjecture difficult to prove because there isn't a tight enough upper bound for prime gaps?
Is it possible to construct a sequence a(n) of odd numbers, with a gap, depending on, and increasing with, n, between a(n+1) and a(n), such that all even integers greater than a given number can be written as the sum of two terms of a(n)? If it could be shown that a(n+1) - a(n) >= the maximal prime gap following the nth prime, would that prove the conjecture?