This approach is only useful when it is needed to guarantee that a number is prime. For prime gap searches that probably means only maximal gap searches where we want to make sure we haven't missed any large gaps. The approach requires knowing all primes up to sqrt(N) so it couldn't be used for very large numbers. It might be useful up to 2[SUP]80[/SUP].

How far have you gotten in your search now? Have you found any new large prime gaps just above 2[SUP]64[/SUP]? Have you proven that 1552 and 1572 are maximal prime gaps?

[QUOTE=Bobby Jacobs;600956]How far have you gotten in your search now? Have you found any new large prime gaps just above 2[SUP]64[/SUP]? Have you proven that 1552 and 1572 are maximal prime gaps?[/QUOTE]
I think that is a valid question. But I don’t think CraigLo would have forgotten to tell us. :smile: 
Well, Craig has not been on this site in a while. Does anybody else know how to prove the new maximal prime gaps?

[QUOTE=Bobby Jacobs;605422]Well, Craig has not been on this site in a while. Does anybody else know how to prove the new maximal prime gaps?[/QUOTE]
it is “simple” each and every prime gap over a certain number (over 1400 or 1300 is a good bet) needs to be verified from 2[SUP]64[/SUP] to 2[SUP]64[/SUP] +2.33 X10[SUP]16[/SUP]. As far as I know ATH had checked up to 2[SUP]64[/SUP] +1.05 X10[SUP]16[/SUP]. The first gaps that are still not known to be a first occurrence are[LIST] *1432 *1444 *1458 *1472 *1474 *1480 *1484 *1492 *1498 *1500 *1496[/LIST]. If anyone know if any of this gaps has been proven to be a first occurrence, please let us know. When the search is completed up to 18470057946260698231 ie 2[SUP]64[/SUP] +2.33 X10[SUP]16[/SUP]. then it will be (hopefully a new maximal gap. 
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