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-   -   Smallest prime of the form a^2^m + b^2^m, m>=14 (

JeppeSN 2018-04-06 17:26


Submitted as [URL=""]A302387[/URL] (not approved yet). /JeppeSN

JeppeSN 2018-12-15 23:24

[QUOTE=Batalov;482574]Aw well, m=16 was too easy. Even a pair for the good measure:

I just discovered these are duplicates at the PRP Top site. If you [URL=""]search for x^(2^16)+y^(2^16)[/URL], the same two numbers were found by Valeryi Kuryshev in Feb 2011.


Batalov 2018-12-16 00:17

Yes, there are many more; I've seen duplicates in other classes before. (Because there are similarly different ways to write values, e.g. using Phi(), or gcd() ... for primitive parts or Aurifeuillean parts. PRP owners [I]should better have[/I] an in-take evaluator and checker.

The bracketed form is hard to search for. You can use "x^?+y^?" and then filter, but that's not the first form that comes to mind.

JeppeSN 2018-12-16 00:35

OK. And still no trace of [URL=""]A291944[/URL](17), the smallest PRP of form xGF(17, a, b) = a^131072 + b^131072. /JeppeSN

Batalov 2018-12-16 01:57

How far did anybody search?

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