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• Jens I don t know how you can go up that high, good lord! Amazing. Thank you for finding (at over 55,000 digits!) what I could never have hoped to. kind
Message 1 of 6 , Jan 3, 2006
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Jens I don't know how you can go up that high, good lord! Amazing.
Thank you for finding (at over 55,000 digits!) what I could never
have hoped to.

kind regards,
Mark

--- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
<jens.k.a@g...> wrote:
>
(snip)

> The smallest a>1 for which a^r + b^s is never prime for
> b = a+/-1, s = r+/-1, and r,s <= a, is a = 13361.
> This assumes prp's for smaller a are really primes.
>
> The cases where prp's above 3000 digits were needed:
> 1252^1155 + 1253^1154 (3578 digits)
> 3319^992 + 3318^991 (3493 digits)
> 9818^765 + 9819^764 (3054 digits)
> 9819^764 + 9818^765 (3054 digits, same prp as for a=9818)
> 10127^888 + 10126^887 (3557 digits)
> 11051^1176 + 11050^1177 (4760 digits)
>
> PrimeForm/GW made prp tests. 13361^13361 has 55126 digits.
> I stopped there but guess there are primes for larger exponents.
>
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