20230109, 20:09  #606  
Sep 2010
Weston, Ontario
241 Posts 
Quote:


20230109, 21:32  #607 
Jul 2003
So Cal
2,621 Posts 
20018^63+63^20018 is also prime.

20230126, 03:57  #608 
Sep 2010
Weston, Ontario
361_{8} Posts 
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.

20230129, 10:15  #609 
Nov 2019
2^{3}·3 Posts 
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].

20230129, 19:54  #610 
Sep 2010
Weston, Ontario
241 Posts 
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 digitlengths. I had guessed that in the greaterthanonemilliondigits range there might be one PRP every 200 digitlengths, 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 1000027digit PRP?

20230201, 10:00  #611 
Nov 2019
2^{3}×3 Posts 

20230208, 18:09  #612 
"Norbert"
Jul 2014
Budapest
5^{3} Posts 
Another new PRP:
21650^43269+43269^21650, 187591 digits. 
20230219, 19:02  #613 
Nov 2019
11000_{2} Posts 
A new PRP:
101645^94522+94522^101645, 505739 digit, index: 6214332272 
20230313, 12:09  #614 
Nov 2019
2^{3}×3 Posts 
A new 1M+ digits PRP:
218767^37314+37314^218767, 1000175 digits, index: 21595765797 
20230313, 17:49  #615 
Sep 2010
Weston, Ontario
11110001_{2} Posts 
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 1000175digit result and your previous 1000027digit result are consecutive PRPs? Or are you just picking random Leyland number pairs constrained by digit size?

20230313, 18:32  #616 
Aug 2020
79*6581e4;3*2539e3
2×359 Posts 
The Top 20 has been updated now. Impressive how the sizes increased with Andreas' open source implementation.

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