Found a factor, sunshine? Embalm and entomb it here! (RU "Выкрасить и выбросить"))

[nordi]

M36919 has a 180.968-bit (55-digit) factor: 2997347544642661833497896836795494793702018162645139063 (P-1,B1=2000000000,B2=401927737170960)


That gets me to the top of the list of P-1 factors for Mersenne numbers! And all thanks to the new version 30.8 of mprime.

[James Heinrich]

[axn]

Nice!

[masser]

Wow! Congrats!

[charybdis]

Originally Posted by nordi

That gets me to the top of the list of P-1 factors for Mersenne numbers! And all thanks to the new version 30.8 of mprime.

Congratulations!

This comes in at 10th place on the all-time P-1 list, i.e. not restricted to Mersennes. You should drop Paul Zimmermann an email; his address is on the page I linked.

[James Heinrich]

Originally Posted by charybdis

This comes in at 10th place on the all-time P-1 list, i.e. not restricted to Mersennes. You should drop Paul Zimmermann an email; his address is on the page I linked.

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 nordi to email him anyways.

[xilman]

Originally Posted by storm5510

This is from GMP-ECM, and an error on my part:

********** 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

This is for M7363 which does not appear in any database I can find. I had intended M4363. Make of it what you will.

Substantially beyond the limits of the 2- Cunningham table.

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

[Batalov]

Originally Posted by nordi

M36919 has a 180.968-bit (55-digit) factor: 2997347544642661833497896836795494793702018162645139063 (P-1,B1=2000000000,B2=401927737170960)


That gets me to the top of the list of P-1 factors for Mersenne numbers! And all thanks to the new version 30.8 of mprime.

That is indeed a good factor!

Cross-post it in the "(Preying for) World Record P-1" thread

[xilman]

Originally Posted by xilman

Substantially beyond the limits of the 2- Cunningham table.

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

For instance:

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

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]

Originally Posted by xilman

For instance:

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

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.

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]

Originally Posted by James Heinrich

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 nordi to email him anyways.

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