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Re: Known pairs vs OEIS A002072

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  • 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 1 of 4 , Mar 10, 2012
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      > 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 2 of 4 , Mar 12, 2012
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        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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