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Re: [PrimeNumbers] Known pairs vs OEIS A002072

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  • Jim White
    I m sorry, I said 227, I really meant 229! ________________________________ From: Jim White  Subject: [PrimeNumbers] Known pairs vs
    Message 1 of 4 , Mar 7, 2012
      I'm sorry, I said 227, I really meant 229!



      ________________________________
      From: Jim White <mathimagics@...>
       Subject: [PrimeNumbers] Known pairs vs OEIS A002072


       

      Having said that, and assuming both A002072 and
      column k=1 of your chain table are "smallest
      known", I do have a new entry for p = 227, having
      found this pair (S, S+1):
       
      S = 15487655655079919751646464

      This was found via a PTE match at
       Q = 395684061 {0, 3, 3}, {1, 1, 4}
       
      Thus S = Q(Q+3)^2 / 4
       

      Jim White
      Canberra 

      ________________________________
      From: Andrey Kulsha <andrey_601@...>
      To: Jim White <mathimagics@...>
      Sent: Wednesday, 7 March 2012, 4:29
      Subject: Re: [PrimeNumbers] Re: 13-chains of consecutive smooth numbers


      
      Any chance of a text export?
          Here we are: http://www.primefan.ru/stuff/math/maxs.txt

          Chain length from 6 to
      16, N up to 10^13.

          Best regards,

          Andrey

      [Non-text portions of this message have been removed]




      [Non-text portions of this message have been removed]
    • Andrey Kulsha
      ... These values are indeed the largest known (there may be larger ones). Doubt is not about smallest but about for all i m . ... For p = 229 we have
      Message 2 of 4 , Mar 10, 2012
        > I wonder if the largest pair list at A002072 should
        > include some statement that certain values are
        > "smallest known" rather than "smallest", as the
        > latter assumes the values can be confirmed in
        > some rigorous manner.

        These values are indeed the largest known
        (there may be larger ones). Doubt is not about
        "smallest" but about "for all i>m".

        > I do have a new entry for p = 229, having
        > found this pair (S, S+1):
        >
        > S = 15487655655079919751646464

        For p = 229 we have 5.2*sqrt(p)-7.7 = 71,
        so I expect N about exp(71), which is much
        larger than your N about exp(58).

        Best regards,

        Andrey
      • Jim White
        This 181-smooth pair popped up in a random search:   S = 90672220863645734556839376   Factors   S   = 2^4, 3^3, 11, 23, 29, 31, 37^2, 73, 97,       
        Message 3 of 4 , Mar 12, 2012
          This 181-smooth pair popped up in a random search:
           
          S = 90672220863645734556839376
           
          Factors
            S   = 2^4, 3^3, 11, 23, 29, 31, 37^2, 73, 97,
                  139^2, 163, 167, 181
            S-1 = 5^4, 13^3, 17, 19, 43, 47, 67^2, 101^2,
                  113^2, 173

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