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Re: Primo proofs

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  • Jose Luis Gomez Pardo
    ... 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 10:44 AM
      --- David Broadhurst <D.Broadhurst@...>
      escribió: > Dear Jose Luis
      >
      > Please see my congratulations in
      >
      >
      http://groups.yahoo.com/group/primenumbers/message/7475


      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
      already completed in early March (the gap had been
      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.

      Now I am hesitating about the possibility of asking
      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
      few years. Thus I am hesitating about this possibility
      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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