Distribution of twin primes

[David Wilson]

Hugo Pfoertner wrote:

The interesting thing is, that I couldn't find more terms in the latter
sequence up to n=46340 (n^2~=32bit signed integer 2.147*10^9). This suggests
the rather bold conjecture, that all intervals beyond [123^2,124^2] contain
at least one twin prime pair. Proving seems impossible. Anybody interested
in extending the checked range?

Maybe not impossible, but whereas this conjecture implies the Twin Primes
conjecture, it will presumably be difficult.
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