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Re: a^b+b^a is PRP!

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  • d.broadhurst@open.ac.uk
    ... Hmm... a^(a-1)+(a-1)^a doesn t look circle cutting (cyclotomic) from here. I think cyclotomy is always a^n-b^n (and if you want the full Monty, set
    Message 1 of 13 , Jun 2, 2001
      Phil Carmody wrote:

      > I noticed that 3 of the entries in the
      > a^b+b^a list had a=b+1.

      Hmm... a^(a-1)+(a-1)^a doesn't look circle cutting
      (cyclotomic) from here. I think cyclotomy is always
      a^n-b^n (and if you want the full Monty, set
      a=(1+sqrt(5))/2 and b=(1-sqrt(5))/2)
      and divide by a-b=sqrt(5) to get a well known integer)

      David
    • Andrey Kulsha
      Hello! ... for me ... Well, I may prove the numbers which have
      Message 2 of 13 , Jun 2, 2001
        Hello!

        Christ wan Willegen wrote:

        >I have no prior Titanix experience, but I think it's time
        for me
        >to give it a try...
        >
        >Andrey, I am willing to use my Athlon-800 for a few days
        >to try to prove them. Select a few large ones, so that I
        >will be busy for a week or so. You yourself (or someone
        >else?) can perhaps take the smaller ones.

        Well, I may prove the numbers which have <=1000 digits.

        But:

        Paul Leyland wrote:

        >Many of the primes were proved by me years ago, and I had
        two in the
        >prime record tables until they were re-catalogued as
        uninteresting.

        Paul, please send us a list of primes you have proven, and
        we'll prove all remaining ones.

        I will prove less than 1000 digit numbers, Christ wan
        Willegen, for example, will prove numbers with 1001..2000
        digits, and someone third (maybe Paul Leyland) will prove
        numbers with >2000 digits.

        Note that 1000-digit prime 289^406+406^289 was proven by
        Paul, and then independently by me as the smallest titanic
        prime of such a kind. The primes 342^343+343^342,
        111^322+322^111, 122^333+333^122, 8^69+69^8 was also proven
        by me nearly 5 months ago; 365^444+444^365 was proven by me
        and Marcel Martin (he found a step with record polynomial
        degree of 100) nearly 3 months ago.

        Waiting for comments.

        Best wishes,

        Andrey
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      • Andrey Kulsha
        Hello! OK, I ll prove all remaining prps with less than 1200 digits, i.e.: 8^519+519^8, 20^471+471^20, 5^1036+1036^5, 56^477+477^56, 98^435+435^98,
        Message 3 of 13 , Jun 4, 2001
          Hello!

          OK, I'll prove all remaining prps with less than 1200
          digits, i.e.:

          8^519+519^8,
          20^471+471^20,
          5^1036+1036^5,
          56^477+477^56,
          98^435+435^98,
          21^782+782^21,
          32^717+717^32,
          365^444+444^365,
          423^436+436^423,
          34^773+773^34.

          Best wishes,

          Andrey
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