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 2022-05-23, 17:05 #2135 nordi   Dec 2016 11110002 Posts 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.
 2022-05-23, 17:12 #2136 James Heinrich     "James Heinrich" May 2004 ex-Northern Ontario 3,733 Posts
 2022-05-23, 17:17 #2137 axn     Jun 2003 33×199 Posts Nice!
 2022-05-23, 18:15 #2138 masser     Jul 2003 Behind BB 3·5·127 Posts Wow! Congrats!
2022-05-23, 18:47   #2139
charybdis

Apr 2020

2·7·53 Posts

Quote:
 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.

2022-05-23, 19:31   #2140
James Heinrich

"James Heinrich"
May 2004
ex-Northern Ontario

3,733 Posts

Quote:
 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.

Last fiddled with by James Heinrich on 2022-05-23 at 19:31

2022-05-23, 20:35   #2141
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

11,369 Posts

Quote:
 Originally Posted by storm5510 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 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.

2022-05-23, 20:39   #2142
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

9,857 Posts

Quote:
 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

2022-05-23, 20:43   #2143
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

101100011010012 Posts

Quote:
 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:
Code:
pcl@thoth:~/Astro/Misc$ecm 10000 GMP-ECM 7.0.4 [configured with GMP 6.2.1, --enable-asm-redc] [ECM] (2^7363-1)/223 Input number is (2^7363-1)/223 (2215 digits) Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17348063569600894463 Step 1 took 838ms Step 2 took 724ms ********** Factor found in step 2: 4816405503271 Found prime factor of 13 digits: 4816405503271 Composite cofactor ((2^7363-1)/223)/4816405503271 has 2202 digits ((2^7363-1)/223)/4816405503271 Input number is ((2^7363-1)/223)/4816405503271 (2202 digits) Using B1=10000, B2=1678960, polynomial x^1, sigma=0:17644336739200299761 Step 1 took 833ms ********** Factor found in step 1: 616318177 Found prime factor of 9 digits: 616318177 Composite cofactor (((2^7363-1)/223)/4816405503271)/616318177 has 2193 digits That was, of course, rather silly. Because we know that 7363 = 37*199 there are some obvious algebraic factors. It was easier for me to type in ((2^7363-1)/223)/4816405503271 than to perform the algebra. 2022-05-25, 02:20 #2144 Dr Sardonicus Feb 2017 Nowhere 26·7·13 Posts Quote:  Originally Posted by xilman For instance: Code: pcl@thoth:~/Astro/Misc$ 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 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.

Last fiddled with by Dr Sardonicus on 2022-05-25 at 02:23 Reason: gifnix topsy

2022-05-28, 14:38   #2145
charybdis

Apr 2020

10111001102 Posts

Quote:
 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?

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