M2673677 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	22.2932	67.6471%	2000000	50000000	0.5169	6.8643%	22.8101	69.8679%	2.2208%
PrimeNet	2⁵⁹	0.0287	62.7119%	11000	200000	0.0024	2.7088%	0.0311	63.7219%	1.0101%
GPU72	2⁶³	0.5969	65.0794%	13000	220000	0.0027	1.6216%	0.5997	65.6456%	0.5663%
Difference	+5	+21.6963	+2.5677%	+1987000	+49780000	+0.5141	+5.2428%	+22.2104	+4.2223%	+4.2223%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2673677	4581237510520018909207	22	71.956	856729797675639 3 × 285576599225213	2021-03-07	3	285576599225213	222.13	1,742,489	3,254,485

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%
2010-12-08T01:27:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.548%
2014-11-25T02:49:00	Jocelyn Larouche	Manual testing	129006	129006		-		-	-	0.014	-	-	0.964%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	161257	161257		-		-	-	0.018	-	-	1.090%
2015-01-30T21:42:00	Jocelyn Larouche	Manual testing	177382	177382		-		-	-	0.020	-	-	1.146%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	195120	195120		-		-	-	0.022	-	-	1.205%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	214632	214632		-		-	-	0.024	-	-	1.265%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	380231	380231		-		-	-	0.043	-	-	1.664%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	418254	418254		-		-	-	0.047	-	-	1.737%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	460079	460079		-		-	-	0.052	-	-	1.811%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	556694	556694		-		-	-	0.062	-	-	1.966%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	612363	612363		-		-	-	0.069	-	-	2.046%
2015-03-17T11:45:00	Jocelyn Larouche	Manual testing	673599	673599		-		-	-	0.075	-	-	2.128%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	815053	815053		-		-	-	0.091	-	-	2.298%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	986213	986213		-		-	-	0.110	-	-	2.474%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	1084834	1084834		-		-	-	0.121	-	-	2.565%
2015-05-22T00:29:00	Jocelyn Larouche	Manual testing	1193317	1193317		-		-	-	0.134	-	-	2.658%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	1312648	1312648		-		-	-	0.147	-	-	2.752%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1443912	1443912		-		-	-	0.162	-	-	2.849%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1588303	1588303		-		-	-	0.178	-	-	2.947%
2015-07-07T18:14:00	Jocelyn Larouche	Manual testing	1747133	1747133		-		-	-	0.196	-	-	3.047%
2016-08-01T15:21:52	Jocelyn Larouche	Manual testing	1747133	3494266	6	-		-	-	0.206	-	-	3.805%
2018-04-09T09:19:52	Jocelyn Larouche	low 4M	2673677	5234266	6	-		-	-	0.315	-	-	4.308%
2019-11-19T03:32:04	masser	Manual testing	2000000	50000000	12	-		-	-	0.517	-	-	6.864%

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	-	-
2009-01-26T23:23:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-19T19:57:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.115	-	-
2013-01-14T11:57:00	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		-	-	1.397	-	-
2016-01-25T14:29:37	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.795	-	-
2017-09-10T15:01:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.590	-	-
2019-04-22T13:11:28	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.18	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.313 GHz-days
Estimated T-Level:	4.450

Digits	B1	Curves	Complete	FacMiss
20	11000	89 / 100	0.890	40.882%
25	50000	89 / 280	0.318	72.729%

New Calculation Method

Total ECM effort:	9.313 GHz-days
Estimated T-Level:	4.450

Digits	B1	Complete	FacMiss
20	11000	2.887	5.577%
25	50000	0.261	77.011%
30	250000	0.016	98.404%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		80	8.274
50000	5000000	4581237510520018909207	2	0.207
50000	6750000		7	0.832

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-06T09:27:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.310
2010-08-12T15:35:00	James Hintz	terri_castor	50000	5000000						3	0.310
2012-12-11T05:16:00	Smurgs	Praca	50000	5000000						3	0.310
2014-12-16T09:07:00	arnaud	srv-630	50000	5000000						3	0.310
2016-02-01T00:25:50	Knapie	FamServ01	50000	5000000						3	0.310
2016-04-17T02:05:19	Jason U	Server7	50000	5000000						3	0.310
2016-10-04T12:51:14	lettp	Home	50000	5000000						3	0.310
2017-07-06T08:19:02	Bruce	eleven	50000	5000000						3	0.310
2017-11-19T21:29:07	Lelikoid	QH	50000	5000000						3	0.310
2018-06-01T23:55:41	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-07-29T00:32:08	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2020-07-21T00:23:25	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.310
2020-07-30T00:36:43	nokno	leo003	50000	5000000						3	0.310
2020-08-03T04:34:23	GAN	LMS-07	50000	5000000						3	0.310
2020-08-11T19:55:21	daveward2005	Dave2	50000	5000000						3	0.310
2020-08-27T04:38:34	daveward2005	Dave2	50000	5000000						7	0.724
2020-09-29T08:57:42	MarkS	desktop-i7	50000	5000000						7	0.724
2020-10-25T22:12:19	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.724
2020-12-01T16:37:14	rextherunt	ice	50000	5000000						7	0.724
2021-01-03T03:30:39	lycorn	colab_DG	50000	6750000						7	0.832
2021-02-07T09:30:26	Zenzoma	AMD3970X	50000	5000000						7	0.724
2021-03-07T22:56:40	mnd9	75211backdoor	50000	5000000	4581237510520018909207	71.956	2	2	8216680990725816	2	0.207

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	D32CFAE8760AD6E3	0.207
2018-07-24T20:45:32	kkmrkkblmbrbk	old	D32CFAE8760AD6E3	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 = 2673677, B2 = 5234266 (P-1 stage 2)

B1 = 2673677 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 1747133, B2 = 3494266 (P-1 stage 2)

B1 = 1747133 (P-1 stage 1)

B1 = 1588303 (P-1 stage 1)

B1 = 1443912 (P-1 stage 1)

B1 = 1312648 (P-1 stage 1)

B1 = 1193317 (P-1 stage 1)

B1 = 1084834 (P-1 stage 1)

B1 = 986213 (P-1 stage 1)

B1 = 815053 (P-1 stage 1)

B1 = 673599 (P-1 stage 1)

B1 = 612363 (P-1 stage 1)

B1 = 556694 (P-1 stage 1)

B1 = 460079 (P-1 stage 1)

B1 = 418254 (P-1 stage 1)

B1 = 380231 (P-1 stage 1)

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

B1 = 214632 (P-1 stage 1)

B1 = 195120 (P-1 stage 1)

B1 = 177382 (P-1 stage 1)

B1 = 161257 (P-1 stage 1)

B1 = 129006 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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