Leyland Primes (x^y+y^x primes and PRPs)

[lghu]

Originally Posted by pxp

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?

In the case of 1M+ digits, I will be able to tell later if there is another PRP that is in the interval between the previous ones or if there is none. At the moment, for example, I know that there are no Leyland primes with digits 1000101 and 1000103, but I still have to wait for 1000102.
In the case of 500K+, this will not be possible.

[pxp]

Originally Posted by lghu

In the case of 1M+ digits, I will be able to tell later if there is another PRP that is in the interval between the previous ones or if there is none. At the moment, for example, I know that there are no Leyland primes with digits 1000101 and 1000103, but I still have to wait for 1000102.
In the case of 500K+, this will not be possible.

Thank you. Please let us know when you have covered the interval to 1000175 so that I may remove the gap that precedes it from my list.

[pxp]

L(79455,73828) @ 386805 digits is a new PRP. This is my first find since May 2022.

[Cybertronic]

Originally Posted by pxp

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.

I have myself create also a xyyx - table , based on your table at Leyland-primes listing

https://pzktupel.de/Primetables/TableXYYX.php

I hope there is no problem. BTW, 104824^5 + 5^104824 should get also a "P"

Are there also a list for x^y-y^x ?

regards

[Cybertronic]

Are there also a list for x^y-y^x ?

Also online , reference Top 10000 PRP
https://pzktupel.de/Primetables/TableXYYX2.php

[Cybertronic]

Originally Posted by Cybertronic

Also online , reference Top 10000 PRP
https://pzktupel.de/Primetables/TableXYYX2.php

New link:
https://pzktupel.de/Primetables/TableLeyland1.php
https://pzktupel.de/Primetables/TableLeyland2.php

[NorbSchneider]

Another new PRP:
23462^35343+35343^23462, 154462 digits.
Hans: chesswanks.com/num/a094133.txt URL can I not reach

[pxp]

Originally Posted by NorbSchneider

chesswanks.com/num/a094133.txt URL can I not reach

Thank you. Hopefully fixed.

[pxp]

L(86206,33381) @ 389953 digits is a new PRP.

[ryanp]

Here's a new one:

300102^59935+59935^300102 is 3-PRP! (41571.6765s+0.0174s)

1,433,792 digits.

[Batalov]

Originally Posted by ryanp

Here's a new one:
300102^59935+59935^300102 (1,433,792 digits)

Nice and large! Congrats!

Records are there to be beaten!

I remember how 15^328574+328574^15 stayed on top for 7 years, but since '21 the Levai team was ruling for a while... you probably ruined their day today