M3110683 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	2⁶⁹	38.3796	68.1159%	3000000	100000000	1.0224	7.4207%	39.4020	70.4820%	2.3660%
PrimeNet	2⁶⁰	0.0494	63.3333%	13000	240000	0.0031	2.6438%	0.0525	64.3027%	0.9694%
GPU72	2⁶⁴	1.1442	65.6250%	14000	240000	0.0032	1.5081%	1.1475	66.1434%	0.5184%
Difference	+5	+37.2354	+2.4909%	+2986000	+99760000	+1.0192	+5.9126%	+38.2546	+4.3385%	+4.3385%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3110683	1444641309387731059463	22	70.291	232206449417657 11 × 13 × 17 × 37 × 2581591931	2019-11-30	37	2581591931	122.02	17.358	32.420

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.202%
2009-07-03T21:40:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.651%
2011-08-24T02:56:00	Squeeky_Squirrel	T7500_2200	105000	2126250		-		-	-	0.027	-	-	2.277%
2016-08-31T03:20:26	Jocelyn Larouche	low4M	105000	4252500	6	-		-	-	0.041	-	-	2.663%
2016-12-28T01:46:00	Jocelyn Larouche	low 4M	126000	126000		-		-	-	0.016	-	-	0.851%
2017-01-30T01:30:36	Jocelyn Larouche	low 4M	163200	163200		-		-	-	0.020	-	-	0.984%
2017-02-04T18:42:46	Jocelyn Larouche	low 4M	195840	195840		-		-	-	0.024	-	-	1.086%
2017-02-18T18:11:41	Jocelyn Larouche	low 4M	235008	2350080	6	-		-	-	0.043	-	-	2.679%
2017-03-13T20:13:53	Jocelyn Larouche	low 4M	282009	2820090	6	-		-	-	0.052	-	-	2.874%
2018-09-04T14:11:23	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	7.421%
2022-02-09T23:47:58	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	6.861%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-03-26T12:49:00	Rob_Dee	twopc	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-21T13:44:00	Squeeky_Squirrel	T7500_2200	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-03T08:41:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.316	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.631	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.201	-	-
2015-06-11T22:04:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.402	-	-
2017-04-11T13:39:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.805	-	-
2019-01-28T14:25:44	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.61	-	-
2021-12-22T09:19:55	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.22	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.920 GHz-days
Estimated T-Level:	23.196

Digits	B1	Curves	Complete	FacMiss
20	11000	179 / 100	1.790	16.546%
25	50000	179 / 280	0.639	52.707%

New Calculation Method

Total ECM effort:	20.920 GHz-days
Estimated T-Level:	23.196

Digits	B1	Complete	FacMiss
20	11000	5.774	0.311%
25	50000	0.522	59.341%
30	250000	0.032	96.837%
35	1000000	0.001	99.853%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		175	20.45
50000	5000000	1444641309387731059463	4	0.467

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-24T02:17:00	Aca Arsov	backo6400	50000	5000000						3	0.351
2011-07-18T14:55:00	sannerud.com	Jens2010	50000	5000000						3	0.351
2013-12-16T08:58:00	arnaud	Chamot18	50000	5000000						3	0.351
2016-05-18T15:36:26	remvad	home	50000	5000000						3	0.351
2017-11-17T07:24:17	Conductor	NataW	50000	5000000						3	0.351
2019-11-30T13:50:54	mnd9	25836	50000	5000000	1444641309387731059463	70.291	4	2	8288432236308002	4	0.467
2019-11-30T16:09:26	mnd9	25836	50000	5000000						10	1.169
2019-11-30T16:27:35	mnd9	25836	50000	5000000						10	1.169
2019-11-30T16:49:14	mnd9	25836	50000	5000000						10	1.169
2019-11-30T18:10:49	mnd9	50871	50000	5000000						10	1.169
2019-11-30T18:16:56	mnd9	50871	50000	5000000						10	1.169
2019-11-30T18:25:50	mnd9	50871	50000	5000000						10	1.169
2019-11-30T23:23:18	mnd9	75204	50000	5000000						10	1.169
2019-11-30T23:46:05	mnd9	75204	50000	5000000						10	1.169
2019-11-30T23:51:30	mnd9	75204	50000	5000000						10	1.169
2019-12-01T14:55:31	mnd9	50869	50000	5000000						10	1.169
2019-12-01T15:38:39	mnd9	50869	50000	5000000						10	1.169
2019-12-01T16:03:41	mnd9	50869	50000	5000000						10	1.169
2019-12-01T16:11:32	mnd9	dlounge	50000	5000000						10	1.169
2019-12-01T17:15:03	mnd9	dlounge	50000	5000000						10	1.169
2019-12-01T18:55:07	mnd9	dlounge	50000	5000000						10	1.169
2019-12-01T19:22:36	mnd9	dlounge	50000	5000000						10	1.169

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	550D7D641684E417	0.265

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 282009, B2 = 2820090 (P-1 stage 2)

B1 = 235008, B2 = 2350080 (P-1 stage 2)

B1 = 105000, B2 = 4252500 (P-1 stage 2)

B1 = 282009 (P-1 stage 1)

B1 = 235008 (P-1 stage 1)

B1 = 105000, B2 = 2126250 (P-1 stage 2)

B1 = 195840 (P-1 stage 1)

B1 = 163200 (P-1 stage 1)

B1 = 126000 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

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

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