M2676139 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	2⁶⁸	22.2727	67.6471%	2000000	50000000	0.5169	6.8650%	22.7896	69.8681%	2.2210%
PrimeNet	2⁵⁹	0.0287	62.7119%	12000	220000	0.0026	2.8385%	0.0313	63.7703%	1.0584%
GPU72	2⁶³	0.5964	65.0794%	13000	220000	0.0027	1.6218%	0.5991	65.6457%	0.5664%
Difference	+5	+21.6763	+2.5677%	+1987000	+49780000	+0.5141	+5.2432%	+22.1905	+4.2224%	+4.2224%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2676139	41236877457008214851153	23	75.126	7704547009144184 2³ × 963068376143023	2020-08-30	8	963068376143023	3,220.8	5,876,309	10,975,308

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.240%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.785%
2010-11-19T22:14:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.268%
2010-12-07T02:49:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.548%
2016-06-12T23:59:49	Jocelyn Larouche	Manual testing	151882	4567500	6	-		-	-	0.044	-	-	3.186%
2016-12-17T04:47:51	Jocelyn Larouche	low 4M	182258	182258		-		-	-	0.020	-	-	1.163%
2016-12-29T21:56:34	Jocelyn Larouche	low 4M	218709	218709		-		-	-	0.024	-	-	1.277%
2017-03-04T18:15:43	Jocelyn Larouche	low 4M	314940	3149400	6	-		-	-	0.053	-	-	3.267%
2018-08-29T01:29:33	Jocelyn Larouche	low 4M	629880	629880		-		-	-	0.071	-	-	2.071%
2018-08-30T21:10:16	Jocelyn Larouche	low 4M	629880	1259760		-		-	-	0.074	-	-	2.681%
2018-09-03T21:22:15	Jocelyn Larouche	low 4M	629880	1889640		-		-	-	0.078	-	-	3.043%
2018-09-04T10:43:02	Jocelyn Larouche	low 4M	629880	2519520		-		-	-	0.082	-	-	3.302%
2019-11-20T04:52:27	masser	Manual testing	2000000	50000000	12	-		-	-	0.517	-	-	6.865%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-31T10:55:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-12T11:01:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.115	-	-
2013-01-14T12:25:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.367	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.734	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.396	-	-
2016-01-25T14:29:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.792	-	-
2017-09-10T15:01:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.585	-	-
2019-04-22T13:11:28	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.17	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.068 GHz-days
Estimated T-Level:	2.450

Digits	B1	Curves	Complete	FacMiss
20	11000	49 / 100	0.490	61.112%
25	50000	49 / 280	0.175	83.919%

New Calculation Method

Total ECM effort:	5.068 GHz-days
Estimated T-Level:	2.450

Digits	B1	Complete	FacMiss
20	11000	1.581	20.584%
25	50000	0.143	86.688%
30	250000	0.009	99.124%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		45	4.655
50000	5000000	41236877457008214851153	4	0.414

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-07-30T17:32:00	Kamil_Górski	thefault	50000	5000000						3	0.310
2010-08-03T12:08:00	Kamil_Górski	thefault	50000	5000000						3	0.310
2012-12-11T05:10:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.310
2014-12-19T11:45:00	arnaud	srv-630	50000	5000000						3	0.310
2016-03-29T03:28:00	Jason U	Server7	50000	5000000						3	0.310
2016-04-17T15:12:41	Jason U	Server7	50000	5000000						3	0.310
2016-10-07T17:27:28	S36049	Wolle5	50000	5000000						3	0.310
2017-07-07T05:50:20	Bruce	eleven	50000	5000000						3	0.310
2017-11-14T03:28:30	Yan Jinzhao	ThinkPad_R400	50000	5000000						3	0.310
2018-06-04T19:20:01	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-08-08T10:34:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2020-07-21T05:50:10	daveward2005	Dave2	50000	5000000						3	0.310
2020-07-27T12:00:20	GAN	LMS-07	50000	5000000						3	0.310
2020-08-04T10:10:03	rextherunt	ice	50000	5000000						3	0.310
2020-08-11T19:16:21	GAN	LMS-18	50000	5000000						3	0.310
2020-08-30T01:56:23	nordi	sweet16	50000	5000000	41236877457008214851153	75.126	4	2	6278478908360695	4	0.414

date	userid	compid	res64	spent (GHz-days)
2000-02-01T00:00:00	ANONYMOUS	v4_computers	6484608759EE563B	0.207
2018-07-25T11:57:38	kkmrkkblmbrbk	old	6484608759EE563B	0.207

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 2000000, B2 = 50000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 629880, B2 = 2519520 (P-1 stage 2)

B1 = 629880, B2 = 1889640 (P-1 stage 2)

B1 = 629880, B2 = 1259760 (P-1 stage 2)

B1 = 629880 (P-1 stage 1)

B1 = 314940, B2 = 3149400 (P-1 stage 2)

B1 = 151882, B2 = 4567500 (P-1 stage 2)

B1 = 314940 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 218709 (P-1 stage 1)

B1 = 182258 (P-1 stage 1)

B1 = 151882 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

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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