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- Thread starter Loren Booda
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CRGreathouse

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This is the of-yet-unproved Twin Prime Conjecture.

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primes separated by only one even number

Do you mean that infinitely many primes separated by the same even number? Or do you mean infinitely many primes separated by a multiple of the same even number? The latter is true.

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CRGreathouse

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Do you mean that infinitely many primes separated by the same even number? Or do you mean infinitely many primes separated by a multiple of the same even number? The latter is true.

I know Elliott-Halberstam implies that (via Goldston-Pintz-Yıldırım), but is it known unconditionally? As far as I know, [itex]g_n>\sqrt{\log p_n}[/itex] for all n sufficiently large has not been disproven.

Oh wait, I just reread what you wrote. The latter is trivially true, since all prime gaps but the first are divisible by 2.

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Do you mean that infinitely many primes separated by the same even number? Or do you mean infinitely many primes separated by a multiple of the same even number? The latter is true.

The number of pairs of primes with a difference of two.

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That would be the said "Twin Primes Conjecture".

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HallsofIvy

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