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• ... escribió: Dear Jose Luis ... http://groups.yahoo.com/group/primenumbers/message/7475 Thank you very much, following your suggestion I have sent a
Message 1 of 1 , Jun 1, 2002
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escribió: > Dear Jose Luis
>
> Please see my congratulations in
>
>

Thank you very much, following your suggestion I have
sent a message to Chris Caldwell. As a matter of fact
the proof of primality of the endpoints of the gap was
found on November, 2001). I informed Paul Leyland who
marked the numbers as proven primes in his top gaps
list. But I was busy with other things and forgot
about it until a week ago in which I also informed
Marcel Martin (and sent him the certificates). Then
Marcel included the primes in his Top 20 Primo list.

But I'm afraid that this gap will not remain for long
in Paul's list, for a couple of days ago I submitted
to him six large gaps between prp's which will push
the proven one out of the list. The largest gap I
found so far popped up almost three weeks ago (it took
more than two weeks to check it on night runs on a
rather slow computer and with a different -and very
slow- method). The gap has length 176392 and is
limited by two 4813-digit prp's which were found with
the help of the CRT. The "relative size" of this gap
is D = 15.91826774.

people for help in trying to prove the primality of
these two prp's. It would be hard work (if it just
were one prime, but two ...) and, on the other hand, I
think that a 200k+ gap is within reach. I believe that
it would be not too difficult obtain such a gap (with
D > 10, of course)using, say, 8000-digit numbers with
the CRT method. However, it is likely that these
numbers could not be proved prime in the near
future--although they probably will be attainable in a
too. On the other hand, if one works with 5000-digit
numbers, a 200k+ gap would have D >17 and this seems
too difficult (but not impossible with luck!). But
increasing the size to 6000 digits would put the 200k+
gaps at around D = 15, which seems feasible (although
not so easy with numbers of this size). So, if I had
time and resources, I would probably start the search
for a 200k+ gap at around 5000 digits and, if not
successful, increase in steps the size of the numbers,
up to 6000 digits if necessary. This would be a
lenghty process and the problem is that the only
powerful computer I have (the Athlon XP1800+ where I
found all those gaps) must also be devoted to other
tasks, so I am not sure ...

Best regards,

Jose Luis.

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