Browse Groups

• 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
View Source
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.
>
Your message has been successfully submitted and would be delivered to recipients shortly.
• Changes have not been saved
Press OK to abandon changes or Cancel to continue editing
• Your browser is not supported
Kindly note that Groups does not support 7.0 or earlier versions of Internet Explorer. We recommend upgrading to the latest Internet Explorer, Google Chrome, or Firefox. If you are using IE 9 or later, make sure you turn off Compatibility View.