M2814103 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	21.1808	67.6471%	5000000	200000000	1.7498	9.1627%	22.9306	70.6115%	2.9644%
PrimeNet	2⁵⁹	0.0273	62.7119%	12000	240000	0.0027	2.9298%	0.0300	63.8043%	1.0925%
GPU72	2⁶³	0.5671	65.0794%	15000	260000	0.0032	1.7914%	0.5703	65.7049%	0.6256%
Difference	+5	+20.6136	+2.5677%	+4985000	+199740000	+1.7466	+7.3713%	+22.3602	+4.9065%	+4.9065%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2814103	6618271406929387425511	22	72.487	1175911366238085 3 × 5 × 37 × 103 × 20570477849	2021-01-05	103	20570477849	510.89	125.51	234.43

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.243%
2010-11-13T11:54:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.211%
2010-11-16T20:18:00	markr	tiny	100000	2100000		-		-	-	0.023	-	-	2.494%
2016-05-12T15:11:31	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.043	-	-	3.187%
2017-07-30T01:18:54	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.067	-	-	3.580%
2019-10-03T23:34:06	masser	Manual testing	2814103	28141030	12	-		-	-	0.470	-	-	6.376%
2020-01-12T15:54:28	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.163%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-02-12T19:02:00	Sturle Sunde	ginglo.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-02-22T00:43:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.349	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.698	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.328	-	-
2016-02-12T10:12:09	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.655	-	-
2017-10-24T17:48:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.311	-	-
2018-12-31T00:56:16	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.62	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.673 GHz-days
Estimated T-Level:	3.200

Digits	B1	Curves	Complete	FacMiss
20	11000	64 / 100	0.640	52.560%
25	50000	64 / 280	0.229	79.534%

New Calculation Method

Total ECM effort:	6.673 GHz-days
Estimated T-Level:	3.200

Digits	B1	Complete	FacMiss
20	11000	2.462	8.530%
25	50000	0.228	79.632%
30	250000	0.014	98.574%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		58	6.048
50000	5000000	6618271406929387425511	6	0.626

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-29T09:08:00	freeshow	dom	50000	5000000						3	0.313
2010-10-27T10:10:00	James Classen	towerofart	50000	5000000						3	0.313
2013-03-28T12:36:00	Donna Noble	PH2x6	50000	5000000						3	0.313
2015-03-26T22:32:00	Bruce	desk16	50000	5000000						3	0.313
2016-02-17T11:35:01	Sintax	cloud	50000	5000000						3	0.313
2016-06-04T01:38:37	Jason U	Server7	50000	5000000						3	0.313
2017-02-19T03:06:40	Bruce	eleven	50000	5000000						3	0.313
2017-08-30T23:31:56	Angel Pescador		50000	5000000						3	0.313
2018-02-14T07:55:56	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2018-12-25T12:09:21	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2020-08-29T23:52:31	J.R. Allen	lapacer	50000	5000000						7	0.730
2020-10-02T08:00:14	mnd9	75204	50000	5000000						7	0.730
2020-10-29T04:34:41	daveward2005	Dave2	50000	5000000						7	0.730
2020-12-03T21:59:21	C.D.B.	i7-6850K	50000	5000000						7	0.730
2021-01-05T15:21:51	Zenzoma	AMD3970X	50000	5000000	6618271406929387425511	72.487	6	2	8496601746484706	6	0.626

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	69B8C6D8F5250DFA	0.217
2018-09-05T00:24:25	kkmrkkblmbrbk	old	69B8C6D8F5250DFA	0.217

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2814103, B2 = 28141030 (P-1 stage 2)

B1 = 2814103 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2100000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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