June 2021

[Yusuf]

Originally Posted by Kebbaj

10 ^ 545 good!
Go to the maximum yusuf.
we compare our max after the solution. if you want?

Sure, I'll let you know what my largest solution is once the challenge ends

[Kebbaj]

Originally Posted by Yusuf

Sure, I'll let you know what my largest solution is once the challenge ends

Ok yusuf.
Thinks.

[Dr Sardonicus]

Originally Posted by Yusuf

Solved it today, largest solution I found so far is greater than 10^545

This is inspiring! My original, stupidly written and embarrassingly slow script would still be running to try to reach that high. It did, however, quickly produce solutions > 10^100 which I submitted in early June.

I later had a simple idea that greatly improved my script. I only pushed to 10^400, though.

But when I saw 10^545, how could I resist pushing further? I can report that, if my improved script is writ right, there are two solutions between 10^545 and 10^600.

[uau]

With Sage, generating all solutions up to 10^1000 was pretty fast (there are 25 including the example solutions). I tried generating one with more digits, and got a solution above 10^9000.

[Dr Sardonicus]

Originally Posted by uau

With Sage, generating all solutions up to 10^1000 was pretty fast (there are 25 including the example solutions). I tried generating one with more digits, and got a solution above 10^9000.

Thanks for giving me a way to check my script! It was easy to adjust it to check up to 10^1000. Lo and behold, 25 solutions!

[0scar]

Originally Posted by uau

With Sage, generating all solutions up to 10^1000 was pretty fast (there are 25 including the example solutions). I tried generating one with more digits, and got a solution above 10^9000.

Your findings below 10^1000 also match mine.
25 solutions up to 10^1000.
34 solutions up to 10^2000.
46 solutions up to 10^3000. Or less?
Last 12 candidates only passed a BPSW test, I stopped primality proving after 10^2000 because APR-CL was becoming too lengthy. Anyway, my aged YAFU implementation can only prove numbers up to 6021 digits, so your finding above 10^9000 is doubly remarkable to me.
I wonder how long did you take to prove it prime, and if you used some code specially written for Leyland numbers.

[axn]

Are people referring to http://www.primefan.ru/xyyxf/primes.html ?

[Dr Sardonicus]

Originally Posted by 0scar

<snip>
I wonder how long did you take to prove it prime, and if you used some code specially written for Leyland numbers.

Heck, I just used BPSW [Pari-GP's ispseudoprime() function]. If any of the "small" Leyland numbers I was looking at had "passed" that test but were actually composite, I reckoned that would already be known. I did state in my submitted solution that the numbers had only "passed" a BPSW test.

I note that Pari-GP had no trouble finding representations of the solutions by the quadratic forms specified.

[uau]

Originally Posted by 0scar

I wonder how long did you take to prove it prime, and if you used some code specially written for Leyland numbers.

I didn't "prove" it prime - in fact I explicitly turned proofs off in Sage to speed things up (I'm not sure why they're enabled by default, seems silly to me). The unrealistic chance that a probabilistic primality test could return a wrong result is a much less relevant worry than the script being buggy, other software error on the machine, or even a hardware failure.

[LaurV]

Originally Posted by axn

Are people referring to ?

Grrr... you kinda spoiled it

[0scar]

Originally Posted by LaurV

Grrr... you kinda spoiled it

Actually, it seems that I spoiled it before. Within this thread, I was the first one to say "Leyland" (should I say "xilman"?)

Wikipedia page about Leyland numbers mentions the largest known Leyland proven primes and references XYYXF's search project.
This forum also has many threads about Leyland prp finding / primality proving.