mersenneforum.org Leyland Primes (x^y+y^x primes)
 Register FAQ Search Today's Posts Mark Forums Read

2023-01-09, 20:09   #606
pxp

Sep 2010
Weston, Ontario

241 Posts

Quote:
 Originally Posted by bur 3^125330 + 125330^3 The certificate is uploaded and verified to/by factordb.
Thanks for this. I try to keep the proven-primes column on my Leyland-primes listing up-to-date but unless it falls just after the contiguous initial stretch I would need a heads-up of its status to notice. At the moment, all Leyland primes < 13300 digits are factor-db proven. Of the larger numbers, 2929^8656+8656^2929 (noted with a K instead of a P) still remains without a certificate at factordb.

 2023-01-09, 21:32 #607 frmky     Jul 2003 So Cal 2,621 Posts 20018^63+63^20018 is also prime.
2023-01-26, 03:57   #608
pxp

Sep 2010
Weston, Ontario

3618 Posts

Quote:
 Originally Posted by lghu My 'Leyland-1M' project found this PRP: 211185^54364+54364^211185 is Fermat and Lucas PRP! 1000027 digits, index: 21589915517 (if my program is correct).
It seems that this is the only Leyland PRP with at least one million decimal digits, but fewer than one million one hundred decimal digits.

2023-01-29, 10:15   #609
lghu

Nov 2019

23·3 Posts

Quote:
 Originally Posted by pxp It seems that this is the only Leyland PRP with at least one million decimal digits, but fewer than one million one hundred decimal digits.
This is not so surprising, since for example there is no Leyland PRP between L(238176,19) and L(65073,48202) [digits 304569 and 304742].

2023-01-29, 19:54   #610
pxp

Sep 2010
Weston, Ontario

241 Posts

Quote:
 Originally Posted by lghu This is not so surprising, since for example there is no Leyland PRP between L(238176,19) and L(65073,48202) [digits 304569 and 304742].
Since we know that there are 63 Leyland PRPs from digits 300000 to 305000, we can say that, in that range, on average there is one PRP every 80 digit-lengths. I had guessed that in the greater-than-one-million-digits range there might be one PRP every 200 digit-lengths, so the surprise really was that there is a solution at all. If I may ask, how many candidates did you look at before finding your 1000027-digit PRP?

2023-02-01, 10:00   #611
lghu

Nov 2019

23×3 Posts

Quote:
 Originally Posted by pxp If I may ask, how many candidates did you look at before finding your 1000027-digit PRP?
I can't say exactly. To test with the same digits, approx. 600-700 Fermat-tests are needed after searching for small prime divisors.

 2023-02-08, 18:09 #612 NorbSchneider     "Norbert" Jul 2014 Budapest 53 Posts Another new PRP: 21650^43269+43269^21650, 187591 digits.
 2023-02-19, 19:02 #613 lghu   Nov 2019 110002 Posts A new PRP: 101645^94522+94522^101645, 505739 digit, index: 6214332272
 2023-03-13, 12:09 #614 lghu   Nov 2019 23×3 Posts A new 1M+ digits PRP: 218767^37314+37314^218767, 1000175 digits, index: 21595765797
2023-03-13, 17:49   #615
pxp

Sep 2010
Weston, Ontario

111100012 Posts

Quote:
 Originally Posted by lghu 218767^37314+37314^218767, 1000175 digits, index: 21595765797
Is your search technique exhaustive? By which I mean, are you able to tell us — now or at some point in the future — that this 1000175-digit result and your previous 1000027-digit result are consecutive PRPs? Or are you just picking random Leyland number pairs constrained by digit size?

2023-03-13, 18:32   #616
bur

Aug 2020
79*6581e-4;3*2539e-3

2×359 Posts

Quote:
 Originally Posted by paulunderwood There have been a few recent ECPP numbers not making their respective top20 tables. I told Prof Caldwell. I guess he is busy retiring. Perhaps someone can email him about these numbers.
The Top 20 has been updated now. Impressive how the sizes increased with Andreas' open source implementation.

 Similar Threads Thread Thread Starter Forum Replies Last Post emily Math 35 2022-12-21 16:32 carpetpool Miscellaneous Math 4 2022-07-14 02:29 Batalov XYYXF Project 57 2022-06-30 17:24 davar55 Puzzles 9 2016-03-15 20:55 troels munkner Miscellaneous Math 4 2006-06-02 08:35

All times are UTC. The time now is 08:38.

Fri Mar 24 08:38:52 UTC 2023 up 218 days, 6:07, 0 users, load averages: 0.67, 0.81, 0.82