M255971 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	116.0831	73.1343%	30000000	10035812696910	5,417.9473	23.4370%	5,534.0304	79.4308%	6.2965%
PrimeNet	2⁴⁰	0.0000	55.0000%	2600	70000	0.0001	14.2534%	0.0001	61.4140%	6.4140%
GPU72	2⁴⁴	0.0000	59.0909%	4500	110000	0.0001	10.1972%	0.0001	63.2625%	4.1716%
Difference	+23	+116.0831	+14.0434%	+29995500	+10035812586910	+5,417.9472	+13.2398%	+5,534.0303	+16.1683%	+16.1683%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
255971	3620433146271791631374063	25	81.582	7071959609236576861 7071959609236576861	2020-10-28	1	7071959609236576861	2,311,208	3.818e+9	7.130e+9
255971	357630485411992687287129073	27	88.209	698576177402894639016 2³ × 3⁴ × 7 × 197 × 307 × 541 × 4706942129	2020-02-09	541	4706942129	351,757,524	2.5410	4.7458
255971	69535498222814385723733792463041	32	105.778	135826906608198557109465120 2⁵ × 3² × 5 × 13 × 29 × 659 × 13418833 × 28293182767	2011-09-21	13418833	28293182767	6.318e+11	15.399	28.527

exponent	prime factors	composite factor	digits	bits*
255971	3620433146271791631374063 357630485411992687287129073	12947772635028487640231584467719616546428734254335 99	52	169.791
255971	3620433146271791631374063 69535498222814385723733792463041	25174862260840046198022200149131595678730845421997 3505583	57	187.360
255971	357630485411992687287129073 69535498222814385723733792463041	24868013982789863606022678831332064258353727709854 349090993	59	193.986
255971	3620433146271791631374063 357630485411992687287129073 69535498222814385723733792463041	90032982105242813841479058542859918826162320152474 687263149806014193602263607114559	83	275.569

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2000-12-14T00:00:00	ANONYMOUS	v4_computers	95000	3800000		-		-	-	0.003	-	-	2.200%
2001-06-17T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.006	-	-	2.721%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.002	-	-	1.559%
2002-08-10T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.004	-	-	2.242%
2003-03-07T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.008	-	-	3.052%
2003-11-08T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.017	-	-	3.979%
2011-02-09T22:33:00	Jocelyn Larouche	Manual testing	2000000	2000000		-		-	-	0.020	-	-	2.609%
2021-09-05T06:34:05	Oliver Kruse	Ollaptop	30000000	3000000000	24	-		-	-	1.901	-	-	12.590%
2022-04-27T03:46:48	Oliver Kruse	Threadripper-PC	30000000	10035812696910		-	skipped known factor: 357630485411992687287129073 skipped known factor: 69535498222814385723733792463041	-	-	5,418	-	-	23.437%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-11-24T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.009	-	-
2000-12-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.019	-	-
2001-02-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.038	-	-
2002-03-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.075	-	-
2022-03-07T05:52:30	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.075	-	-
2009-01-01T20:16:00	Sturle Sunde	gobi.ifi	2⁵⁸	2⁵⁹		-	-	0.150	-	-
2009-01-26T05:01:00	Sturle Sunde	ginjtje.ifi	2⁵⁹	2⁶⁰		-	-	0.300	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.380 GHz-days
Estimated T-Level:	26.969

Digits	B1	Curves	Complete	FacMiss
20	11000	535 / 100	5.350	0.462%
25	50000	535 / 280	1.911	14.747%
30	250000	252 / 640	0.394	67.431%

New Calculation Method

Total ECM effort:	11.380 GHz-days
Estimated T-Level:	26.969

Digits	B1	Complete	FacMiss
20	11000	30.129	0.000%
25	50000	3.885	2.056%
30	250000	0.381	68.304%
35	1000000	0.030	97.061%
40	3000000	0.002	99.807%

ECM Summary

B1	B2	factor	curves	GHz-days
		69535498222814385723733792463041	1	0.00000e+0
50000	5000000		283	2.062
250000	25000000		222	8.088
250000	25000000	3620433146271791631374063	6	0.219
250000	25000000	357630485411992687287129073	3	0.109
250000	38500000		21	0.902

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-09T07:43:00	George Woltman	D_P4Debug	50000	5000000						1	0.007
2007-08-17T12:33:00	ANONYMOUS	Bayes	50000	5000000						1	0.007
2007-08-29T08:02:00	Team_Bundu	bundu1	50000	5000000						1	0.007
2007-09-10T23:17:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-10-09T11:12:00	ANONYMOUS	minister	50000	5000000						1	0.007
2007-12-27T14:23:00	Steve Scott	Abit	50000	5000000						1	0.007
2007-12-27T16:18:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-12-27T16:41:00	Steve Scott	Abit	50000	5000000						1	0.007
2007-12-27T17:15:00	Steve Scott	Abit	50000	5000000						1	0.007
2007-12-27T18:01:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-12-27T18:07:00	Steve Scott	Asus-1	50000	5000000						1	0.007
2008-01-08T19:28:00	Steve Scott	Asus-1	50000	5000000						3	0.022
2008-08-14T01:16:00	Sturle Sunde	v17	50000	5000000						3	0.022
2008-09-16T15:37:00	Sturle Sunde	v23	50000	5000000						3	0.022
2008-10-14T21:50:00	Sturle Sunde	v1	50000	5000000						3	0.022
2008-11-15T05:01:00	Sturle Sunde	v22	50000	5000000						3	0.022
2008-12-06T05:07:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-01-12T18:30:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-02-11T20:45:00	Sturle Sunde	v22	50000	5000000						3	0.022
2009-03-25T10:26:00	Carsten Kossendey	durandal	50000	5000000						1	0.007
2009-03-25T11:55:00	BigBrother	Miniluv	50000	5000000						3	0.022
2009-03-25T20:07:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-04-07T10:35:00	Carsten Kossendey	Manual testing	50000	5000000						1	0.007
2009-04-13T23:58:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-04-19T00:13:00	linded	kctz73a	50000	5000000						3	0.022
2009-04-21T23:19:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-04-26T00:15:00	linded	kctz74z	50000	5000000						3	0.022
2009-04-29T02:17:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-05-03T01:07:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-05-07T16:31:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-05-11T01:04:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-05-14T01:48:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-05-18T05:09:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-05-22T23:04:00	ClknGo Software	cngws2	50000	5000000						3	0.022
2009-05-26T21:07:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-05-30T04:42:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-06-03T15:13:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-06-07T16:15:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-06-11T21:15:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-06-11T22:26:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-06-24T00:21:00	carlos56	tesa11	50000	5000000						3	0.022
2009-07-04T06:09:00	WileECoyote	otto4	50000	5000000						3	0.022
2009-07-16T21:42:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-07-30T18:14:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-08-12T16:21:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-08-19T22:16:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-08-27T17:02:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-08-30T16:17:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-09-02T20:55:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-09-06T16:07:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-09-10T01:44:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-09-13T01:06:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-09-16T05:04:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-09-19T19:30:00	linded	23G4692-Lib1	50000	5000000						3	0.022
2009-09-23T03:23:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-09-26T03:01:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-09-29T23:05:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-10-04T08:35:00	ClknGo Software	cngws2	50000	5000000						3	0.022
2009-10-11T14:48:00	Lackó	Iroda_Andras	50000	5000000						3	0.022
2009-10-15T14:36:00	Lackó	Iroda_Andras	50000	5000000						3	0.022
2009-10-18T05:33:00	ANONYMOUS	v23	50000	5000000						3	0.022
2009-10-22T00:10:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-10-24T15:43:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-10-27T17:33:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-10-29T20:31:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-11-01T19:56:00	ANONYMOUS	v23	50000	5000000						3	0.022
2009-11-04T17:34:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-11-07T15:32:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-11-13T15:23:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-11-18T00:19:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-11-21T02:50:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-11-24T18:07:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-11-24T23:25:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-11-27T20:24:00	ClknGo Software	cngws2	50000	5000000						3	0.022
2009-12-01T00:23:00	ANONYMOUS	v23	50000	5000000						3	0.022
2009-12-03T23:16:00	ClknGo Software	cngws2	50000	5000000						3	0.022
2009-12-08T19:00:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-12-10T18:41:00	Dmitry B. Khachaturov	dix-dubna	50000	5000000						3	0.022
2009-12-13T15:18:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-12-16T23:20:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-12-23T12:35:00	Lackó	Iroda_Andras	50000	5000000						3	0.022
2009-12-29T02:04:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-01-04T20:24:00	Sturle Sunde	v23	50000	5000000						3	0.022
2010-01-08T15:16:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-01-12T22:00:00	Sturle Sunde	v23	50000	5000000						3	0.022
2010-01-15T22:42:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-01-19T21:35:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-01-23T15:52:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-01-26T20:08:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-02-01T22:35:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-02-04T19:41:00	Sturle Sunde	v23	50000	5000000						3	0.022
2010-02-07T22:57:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-02-11T15:30:00	Sturle Sunde	v23	50000	5000000						3	0.022
2010-02-15T17:35:00	Sturle Sunde	v23	50000	5000000						3	0.022
2010-02-19T13:20:00	BOM	C2Q-2667	50000	5000000						3	0.022
2010-02-24T17:58:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-03-05T01:13:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-03-11T15:59:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-04-12T14:49:00	James Hintz	NEW_OMFG	50000	5000000						3	0.022
2010-04-12T15:47:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-04-12T16:44:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-04-12T23:22:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-04-12T23:34:00	Sturle Sunde	v21	50000	5000000						3	0.022
2010-04-14T16:47:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-04-18T06:49:00	James Hintz	04_122109	250000	25000000						3	0.109
2010-05-07T19:21:00	ANONYMOUS	v23	250000	25000000						3	0.109
2010-05-22T15:44:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-06-03T03:05:00	David Bessell	T413	250000	25000000						3	0.109
2010-06-15T13:57:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-07-13T04:31:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-08-21T00:51:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-09-13T10:58:00	David Bessell	T413	250000	25000000						3	0.109
2010-10-07T17:25:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-10-26T01:04:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-11-17T18:18:00	Sturle Sunde	v23	250000	25000000						3	0.109
2010-12-09T01:41:00	Sturle Sunde	v21	250000	25000000						3	0.109
2010-12-31T15:16:00	David Bessell	T413	250000	25000000						3	0.109
2011-01-22T11:59:00	David Bessell	T413	250000	25000000						3	0.109
2011-02-10T02:08:00	Sturle Sunde	v21	250000	25000000						3	0.109
2011-03-09T16:38:00	Sturle Sunde	v23	250000	25000000						3	0.109
2011-04-10T04:57:00	Sturle Sunde	v23	250000	25000000						3	0.109
2011-05-09T04:50:00	Sturle Sunde	v21	250000	25000000						3	0.109
2011-05-25T18:05:00	Sturle Sunde	v21	250000	25000000						3	0.109
2011-06-11T04:18:00	Sturle Sunde	v23	250000	25000000						3	0.109
2011-08-25T14:48:00	Sturle Sunde	v21	250000	25000000						3	0.109
2011-09-21T22:20:00	David Bessell	T413			69535498222814385723733792463041	105.778		1		1	-
2020-01-23T17:57:38	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-26T03:36:46	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-28T16:37:20	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-31T10:13:50	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-03T10:12:42	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-06T12:45:45	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-09T20:09:38	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000	357630485411992687287129073	88.209	3	2	8180100874021733	3	0.109
2020-02-13T12:33:11	kracker	O0	250000	25000000						3	0.109
2020-02-17T07:21:06	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-20T09:44:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-24T02:34:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-27T08:45:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-02T05:37:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-06T22:10:48	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-12T19:19:52	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-18T10:10:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-27T18:58:37	-Anonymous-	aws-nano	250000	25000000						3	0.109
2020-04-14T20:32:31	Oliver Kruse	IOS-1	250000	25000000						3	0.109
2020-04-30T03:50:19	Greg	azure4	250000	25000000						3	0.109
2020-05-04T08:17:05	Greg Hogan	azure4	250000	25000000						3	0.109
2020-05-14T10:16:04	kracker	O0	250000	25000000						3	0.109
2020-06-01T21:48:20	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						3	0.109
2020-06-15T09:53:02	TJAOI	Manual testing	250000	25000000						13	0.474
2020-08-12T11:15:57	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						3	0.109
2020-09-25T00:57:56	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2020-10-28T10:11:43	nordi	sweet16	250000	25000000	3620433146271791631374063	81.582	6	2	2853976561509813	6	0.219
2020-11-07T08:08:09	nordi	sweet16	250000	25000000						7	0.255
2020-12-30T09:58:51	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						7	0.255
2021-01-26T23:44:08	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2021-03-06T09:21:24	Deufo	Ryzen2600	250000	38500000						7	0.301
2021-04-29T21:54:50	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.255
2021-06-20T11:28:44	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2021-07-31T10:17:16	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.255
2021-09-03T00:23:19	Dylan Delgado	colab	250000	38500000						7	0.301
2021-10-11T05:29:56	JackBlock	school1	250000	25000000						7	0.255
2021-12-04T00:16:27	volki	home	250000	25000000						7	0.255
2022-02-12T04:58:27	Corey	tab	250000	25000000						7	0.255
2022-04-02T05:01:58	Dylan Delgado	colab	250000	38500000						7	0.301
2022-05-24T15:21:44	Massimo Cappelli (ik5pwa)	maxlinux_8	250000	25000000						7	0.255

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront