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.

>