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nordi 2022-05-23 17:05

[M]M36919[/M] has a 180.968-bit (55-digit) factor: [URL="https://www.mersenne.ca/M36919"]2997347544642661833497896836795494793702018162645139063[/URL] (P-1,B1=2000000000,B2=401927737170960)


That gets me to the top of the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]list of P-1 factors for Mersenne numbers[/URL]! And all thanks to the new version 30.8 of mprime.


:maybeso::wacky:

James Heinrich 2022-05-23 17:12

:groupwave: :party:

axn 2022-05-23 17:17

Nice!

masser 2022-05-23 18:15

Wow! Congrats!

charybdis 2022-05-23 18:47

[QUOTE=nordi;606342] That gets me to the top of the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]list of P-1 factors for Mersenne numbers[/URL]! And all thanks to the new version 30.8 of mprime.[/QUOTE]

Congratulations!

This comes in at 10th place on the [URL="https://members.loria.fr/PZimmermann/records/Pminus1.html"]all-time P-1 list[/URL], i.e. not restricted to Mersennes. You should drop Paul Zimmermann an email; his address is on the page I linked.

James Heinrich 2022-05-23 19:31

[QUOTE=charybdis;606354]This comes in at 10th place on the [URL="https://members.loria.fr/PZimmermann/records/Pminus1.html"]all-time P-1 list[/URL], i.e. not restricted to Mersennes. You should drop Paul Zimmermann an email; his address is on the page I linked.[/QUOTE]Record-size Mersenne factors are automatically reported to Paul Zimmerman (and Richard Brent for ECM) during the nightly data sync. The codepath for auto-reporting P-1 factors hasn't yet been tested (nobody has found a sufficiently large P-1 factor since I wrote the code in 2020) so tonight will be its test. Wouldn't hurt for [i]nordi[/i] to email him anyways.

xilman 2022-05-23 20:35

[QUOTE=storm5510;603269]This is from GMP-ECM, and an error on my part:

[CODE]********** Factor found in step 2: 223
2022-04-04 09:43:03.243 Found prime factor of 3 digits: 223
2022-04-04 09:43:03.243 Composite cofactor (2^7363-1)/223 has 2215 digits[/CODE]

This is for M7363 which does not appear in any database I can find. I had intended M4363. Make of it what you will.[/QUOTE]Substantially beyond the limits of the 2- Cunningham table.

Don't let that stop you from trying to find more factors though.

Batalov 2022-05-23 20:39

[QUOTE=nordi;606342][M]M36919[/M] has a 180.968-bit (55-digit) factor: [URL="https://www.mersenne.ca/M36919"]2997347544642661833497896836795494793702018162645139063[/URL] (P-1,B1=2000000000,B2=401927737170960)


That gets me to the top of the [URL="https://www.mersenne.ca/userfactors/pm1/1/bits"]list of P-1 factors for Mersenne numbers[/URL]! And all thanks to the new version 30.8 of mprime.
[/QUOTE]
That is indeed a good factor!

Cross-post it in the "([I]Preying for[/I]) World Record P-1" thread :rolleyes:

xilman 2022-05-23 20:43

[QUOTE=xilman;606363]Substantially beyond the limits of the 2- Cunningham table.

Don't let that stop you from trying to find more factors though.[/QUOTE]For instance:
[code]
pcl@thoth:~/Astro/Misc$ ecm 10000
GMP-ECM 7.0.4 [configured with GMP 6.2.1, --enable-asm-redc] [ECM]
(2^7363-1)/223
Input number is (2^7363-1)/223 (2215 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17348063569600894463
Step 1 took 838ms
Step 2 took 724ms
********** Factor found in step 2: 4816405503271
Found prime factor of 13 digits: 4816405503271
Composite cofactor ((2^7363-1)/223)/4816405503271 has 2202 digits
((2^7363-1)/223)/4816405503271
Input number is ((2^7363-1)/223)/4816405503271 (2202 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17644336739200299761
Step 1 took 833ms
********** Factor found in step 1: 616318177
Found prime factor of 9 digits: 616318177
Composite cofactor (((2^7363-1)/223)/4816405503271)/616318177 has 2193 digits

[/code]That was, of course, rather silly. Because we know that 7363 = 37*199 there are some obvious algebraic factors. It was easier for me to type in ((2^7363-1)/223)/4816405503271 than to perform the algebra.

Dr Sardonicus 2022-05-25 02:20

[QUOTE=xilman;606367]For instance:
[code]
pcl@thoth:~/Astro/Misc$ ecm 10000
GMP-ECM 7.0.4 [configured with GMP 6.2.1, --enable-asm-redc] [ECM]
(2^7363-1)/223
Input number is (2^7363-1)/223 (2215 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17348063569600894463
Step 1 took 838ms
Step 2 took 724ms
********** Factor found in step 2: 4816405503271
Found prime factor of 13 digits: 4816405503271
Composite cofactor ((2^7363-1)/223)/4816405503271 has 2202 digits
((2^7363-1)/223)/4816405503271
Input number is ((2^7363-1)/223)/4816405503271 (2202 digits)
Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17644336739200299761
Step 1 took 833ms
********** Factor found in step 1: 616318177
Found prime factor of 9 digits: 616318177
Composite cofactor (((2^7363-1)/223)/4816405503271)/616318177 has 2193 digits

[/code]That was, of course, rather silly. Because we know that 7363 = 37*199 there are some obvious algebraic factors. It was easier for me to type in ((2^7363-1)/223)/4816405503271 than to perform the algebra.[/QUOTE]For an odd prime p, any prime factor q of 2^p - 1 is of the form 2*k*p+1, k integer; in particular, q > p.

This leads to a ludicrous proof of compositeness and factorization:

The fact that 223 divides 2^7363 - 1 though 223 < 7363 proves that 7363 is composite.

Factoring 223 - 1 or 222, we get the prime factors 2, 3, and 37. And 37 divides 7363, the quotient being 199.

Curiously, the factor 4816405503271 divides the "primitive part" (2^7363 - 1)/(2^37 - 1)/(2^199 - 1) of 2^7363 - 1. The cofactor (2^7363 - 1)/(2^37 - 1)/(2^199 - 1)/4816405503271 is composite.

charybdis 2022-05-28 14:38

[QUOTE=James Heinrich;606358]Record-size Mersenne factors are automatically reported to Paul Zimmerman (and Richard Brent for ECM) during the nightly data sync. The codepath for auto-reporting P-1 factors hasn't yet been tested (nobody has found a sufficiently large P-1 factor since I wrote the code in 2020) so tonight will be its test. Wouldn't hurt for [i]nordi[/i] to email him anyways.[/QUOTE]

I see that Paul's list still hasn't ben updated. Did the code work correctly?


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