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-   -   Leyland Primes (x^y+y^x primes) (https://www.mersenneforum.org/showthread.php?t=19347)

lghu 2021-09-09 08:18

I found a Leyland PRP with more than 500,000 digits, details later...

lghu 2021-09-11 12:38

pfgw64: ((100263^98600)+(98600^100263)) is 3-PRP! (7167.1435s+0.0099s)

ecpp-dj -bpsw: ((100263**98600)+(98600**100263)) PROBABLE PRIME (135355 sec)

Gabor Levai

paulunderwood 2021-09-11 12:43

[QUOTE=lghu;587688]pfgw64: ((100263^98600)+(98600^100263)) is 3-PRP! (7167.1435s+0.0099s)

ecpp-dj -bpsw: ((100263**98600)+(98600**100263)) PROBABLE PRIME (135355 sec)

Gabor Levai[/QUOTE]

Although it good to us another library, for numbers of this size you can use the -tc switch of PFGW to get a combined Fermat+Lucas result, which is much quicker.

Congrats for such a huge find.

pxp 2021-09-12 09:33

100263^98600+98600^100263,500702

If you haven't already done so, you should submit this to PRPTop, [URL="http://www.primenumbers.net/prptop/submit.php"]here[/URL].

lghu 2021-09-13 08:39

[QUOTE=paulunderwood;587691]Although it good to us another library, for numbers of this size you can use the -tc switch of PFGW to get a combined Fermat+Lucas result, which is much quicker.

Congrats for such a huge find.[/QUOTE]

Thanks.
((100263^98600)+(98600^100263)) is Fermat and Lucas PRP! (37359.5544s+0.0101s)

NorbSchneider 2021-11-05 10:48

Another new PRP:
35820^35899+35899^35820, 163489 digits.

pxp 2021-11-06 02:51

I have now finished testing the Leyland numbers in the interval from L(300999,10) to L(301999,10) and have found therein 12 PRPs. Next interval is L(301999,10) - L(302999,10).

lghu 2021-11-09 12:19

A prime number: 100207, a square number: 99856 (=316^2), a PRP: 100207^99856+99856^100207.


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