M2741303 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	21.7433	67.6471%	2700000	84000000	0.7984	7.6742%	22.5417	70.1299%	2.4828%
PrimeNet	2⁵⁹	0.0280	62.7119%	12000	220000	0.0026	2.8508%	0.0306	63.7749%	1.0630%
GPU72	2⁶³	0.5822	65.0794%	14000	240000	0.0029	1.7080%	0.5852	65.6758%	0.5964%
Difference	+5	+21.1611	+2.5677%	+2686000	+83760000	+0.7955	+5.9662%	+21.9566	+4.4541%	+4.4541%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2741303	480085899505203423209070103	27	88.633	87565274525509114317 3 × 279553 × 104411059233263	2021-03-16	279553	104411059233263	31,167,677	637,080	1,189,888

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.241%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	225000		-		-	-	0.003	-	-	0.798%
2010-12-19T21:44:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.269%
2010-12-29T20:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.373%
2011-01-20T22:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.539%
2011-04-29T10:25:00	James Heinrich	WHS	185000	4625000		-		-	-	0.048	-	-	3.314%
2016-11-04T21:52:12	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.674%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-04-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:20	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-31T02:41:00	Sturle Sunde	zumthor.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-07T15:17:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.112	-	-
2013-01-14T12:27:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.358	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.716	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.363	-	-
2016-02-03T11:43:36	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.726	-	-
2017-10-05T11:09:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.452	-	-
2019-02-15T01:31:29	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.90	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.929 GHz-days
Estimated T-Level:	4.300

Digits	B1	Curves	Complete	FacMiss
20	11000	86 / 100	0.860	42.133%
25	50000	86 / 280	0.307	73.514%

New Calculation Method

Total ECM effort:	8.929 GHz-days
Estimated T-Level:	4.300

Digits	B1	Complete	FacMiss
20	11000	2.774	6.240%
25	50000	0.251	77.823%
30	250000	0.015	98.468%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		81	8.410
50000	5000000	480085899505203423209070103	5	0.519

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-13T13:06:00	oodaira	Win02	50000	5000000						3	0.311
2010-09-02T15:39:00	James Classen	towerofart	50000	5000000						3	0.311
2013-02-24T13:02:00	Donna Noble	PH2x6	50000	5000000						3	0.311
2015-03-06T23:05:00	S36049	Wolle5	50000	5000000						3	0.311
2016-02-10T19:20:59	Bruce	Desk8	50000	5000000						3	0.311
2016-05-10T08:12:30	lettp	Home	50000	5000000						3	0.311
2016-12-27T03:46:03	Bruce	eleven	50000	5000000						3	0.311
2017-07-22T11:10:15	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.311
2017-12-17T20:04:33	Sebastian Hornbostel	V2	50000	5000000						3	0.311
2018-09-05T07:23:12	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2020-08-02T13:39:38	Claude Portenier	Petit-Idiot	50000	5000000						3	0.311
2020-08-07T00:55:29	GAN	LMS-14	50000	5000000						3	0.311
2020-08-15T20:12:04	mnd9	50871b	50000	5000000						3	0.311
2020-09-10T00:52:44	IanGlencross	glenx24	50000	5000000						7	0.727
2020-10-12T13:50:30	nordi	sweet16	50000	5000000						7	0.727
2020-11-08T07:04:02	mnd9	27016b	50000	5000000						7	0.727
2020-12-14T23:37:34	daveward2005	Dave2	50000	5000000						7	0.727
2021-01-15T20:32:54	mnd9	office2	50000	5000000						7	0.727
2021-02-16T01:20:07	Brett Walker	brain	50000	5000000						7	0.727
2021-03-16T05:47:24	mnd9	office2	50000	5000000	480085899505203423209070103	88.633	5	2	7323566366450318	5	0.519

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	29B586CE214AF8A5	0.212
2018-08-11T18:24:49	kkmrkkblmbrbk	old	29B586CE214AF8A5	0.212

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 185000, B2 = 4625000 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 225000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

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