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(n+1)^p-n^p for the difficult case n=137

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  • j_chrtn
    Hi group, 138^196873-137^196873 is PRP for bases 2, 3, 5, 7, 11, 13, 17, 19, 31, 71 and 101. This number has 421285 digits. Moreover, 138^p-137^p is composite
    Message 1 of 2 , Dec 12, 2009
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      Hi group,

      138^196873-137^196873 is PRP for bases 2, 3, 5, 7, 11, 13, 17, 19, 31, 71 and 101.

      This number has 421285 digits.

      Moreover, 138^p-137^p is composite for all primes p < 196873 !

      This later result should however better be double checked, since it took me more than 2 years to check all p <= 196873; and I can't be absolutely sure I made no mistake during this long period.

      Any volunteer for the double check task ? ;-)

      Best regards,

      Jean-Louis
    • mikeoakes2
      ... Sterling work, Jean-Louis! (David should like this:-) Mike
      Message 2 of 2 , Dec 12, 2009
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        --- In primenumbers@yahoogroups.com, "j_chrtn" <j_chrtn@...> wrote:
        >
        > Hi group,
        >
        > 138^196873-137^196873 is PRP for bases 2, 3, 5, 7, 11, 13, 17, 19, 31, 71 and 101.
        >
        > This number has 421285 digits.
        >
        > Moreover, 138^p-137^p is composite for all primes p < 196873 !
        >
        > This later result should however better be double checked, since it took me more than 2 years to check all p <= 196873; and I can't be absolutely sure I made no mistake during this long period.
        >
        > Any volunteer for the double check task ? ;-)

        Sterling work, Jean-Louis!
        (David should like this:-)

        Mike
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