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2021-06-24, 23:40   #12
Yusuf

Jan 2020

23 Posts

Quote:
 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

2021-06-25, 08:19   #13
Kebbaj

"Kebbaj Reda"
May 2018
Casablanca, Morocco

2·47 Posts

Quote:
 Originally Posted by Yusuf Sure, I'll let you know what my largest solution is once the challenge ends
Ok yusuf.
Thinks.

2021-06-25, 14:16   #14
Dr Sardonicus

Feb 2017
Nowhere

210·5 Posts

Quote:
 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.

 2021-06-25, 18:57 #15 uau   Jan 2017 23×3×5 Posts 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.
2021-06-25, 20:54   #16
Dr Sardonicus

Feb 2017
Nowhere

210·5 Posts

Quote:
 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!

2021-06-26, 04:41   #17
0scar

Jan 2020

22·32 Posts

Quote:
 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.

Last fiddled with by 0scar on 2021-06-26 at 04:43

 2021-06-26, 06:45 #18 axn     Jun 2003 5,179 Posts Are people referring to http://www.primefan.ru/xyyxf/primes.html ?
2021-06-26, 12:14   #19
Dr Sardonicus

Feb 2017
Nowhere

210×5 Posts

Quote:
 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.
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.

2021-06-26, 21:46   #20
uau

Jan 2017

1708 Posts

Quote:
 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.

2021-06-27, 02:37   #21
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

24×613 Posts

Quote:
 Originally Posted by axn Are people referring to ?
Grrr... you kinda spoiled it

2021-07-01, 03:25   #22
0scar

Jan 2020

1001002 Posts

Quote:
 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.

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