M2722879 Mersenne number exponent details

is 2 ^2722879 - 1

has 819669 decimal digits

takes 0.210 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	21.8904	67.6471%	600000	6000000	0.1001	4.0829%	21.9905	68.9680%	1.3209%
PrimeNet	2⁵⁹	0.0282	62.7119%	12000	220000	0.0026	2.8474%	0.0308	63.7736%	1.0617%
GPU72	2⁶³	0.5862	65.0794%	14000	220000	0.0028	1.6640%	0.5890	65.6604%	0.5811%
Difference	+5	+21.3042	+2.5677%	+586000	+5780000	+0.0973	+2.4189%	+21.4016	+3.3076%	+3.3076%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2722879	241440084786858833248903	24	77.676	44335441418230269 3² × 29 × 169867591640729	2020-10-22	29	169867591640729	20,606	1,036,473	1,935,843

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	-	-	0.241%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.788%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.269%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.372%
2011-01-18T22:18:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.538%
2011-02-23T15:18:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.081	-	-	3.994%
2018-08-20T10:32:22	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.100	-	-	4.083%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:20	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-31T19:35:00	Sturle Sunde	gouache.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-16T01:26:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.113	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.361	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.721	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.372	-	-
2016-01-31T12:58:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.744	-	-
2017-10-05T11:09:27	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.489	-	-
2019-02-12T01:22:20	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.98	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.808 GHz-days
Estimated T-Level:	2.800

Digits	B1	Curves	Complete	FacMiss
20	11000	56 / 100	0.560	56.960%
25	50000	56 / 280	0.200	81.844%

New Calculation Method

Total ECM effort:	5.808 GHz-days
Estimated T-Level:	2.800

Digits	B1	Complete	FacMiss
20	11000	1.806	16.424%
25	50000	0.163	84.937%
30	250000	0.010	99.000%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		53	5.497
50000	5000000	241440084786858833248903	3	0.311

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-09T12:25:00	oodaira	Win02	50000	5000000						3	0.311
2010-08-23T00:50:00	James Hintz	ryan	50000	5000000						3	0.311
2013-02-16T20:04:00	Jacques MOLNE	Old_faithfull	50000	5000000						3	0.311
2015-02-22T12:40:00	Jason U	Server7	50000	5000000						3	0.311
2016-02-06T17:36:31	Bruce	Desk8	50000	5000000						3	0.311
2016-05-04T16:50:42	Jason U	Server7	50000	5000000						3	0.311
2016-11-28T00:13:37	deo2016	4CPU.deo2016	50000	5000000						3	0.311
2017-07-19T08:16:33	Sebastian Hornbostel	V2	50000	5000000						3	0.311
2017-12-06T21:33:42	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2018-07-30T10:12:53	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2019-11-02T07:53:21	monsted	rootweiler	50000	5000000						3	0.311
2020-08-01T21:17:51	GAN	LMS-07	50000	5000000						3	0.311
2020-08-09T15:16:42	GAN	LMS-04	50000	5000000						3	0.311
2020-08-23T14:01:36	GAN	KA-AC	50000	5000000						7	0.726
2020-09-25T03:26:34	Chang Chia-Tche	ex-ctcpc	50000	5000000						7	0.726
2020-10-22T03:08:22	mnd9	25836b	50000	5000000	241440084786858833248903	77.676	3	2	7108029175611602	3	0.311

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-08T00:00:00	ANONYMOUS	v4_computers	C658D985E699EBD0	0.210
1999-07-12T00:00:00	ANONYMOUS	v4_computers	C658D985E699EBD0	0.210
2018-08-06T13:51:49	kkmrkkblmbrbk	old	C658D985E699EBD0	0.210

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-22T14:08:03

mrh

lanai

241440084786858833248903

08A020F664DEE268

2020-10-22T16:59:33

oodaira

com2

241440084786858833248903

08A020F664DEE268

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 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-10-22T16:59:33+00:00

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