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@JeremyRouse That is great news for me (and definitevely an answer to my question - you should add it as an answer), could you please point me to some reference about the informations you used in your deduction?
Thanks @jmc, are there no solutions between the primes 37 and 8929? Futhermore, all the primes you found are congruent to 1 mod 12, so the class of primes congruent to 7 mod (12) seems to be outside of it (a guilible mathematician would say). Any ideas?
