M634 211 Mersenne number exponent details

is 2 ⁶³⁴²¹¹ - 1

has 190917 decimal digits

takes 0.010 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
Actual	2⁶⁹	188.2446	71.0145%	51000000	728120893500	875.0704	19.6598%	1,063.3150	76.7130%
Target	2⁴⁴	0.0000	54.5455%	11000	3200000	0.0041	15.9126%	0.0041	61.7784%
Difference	+25	+188.2446	+16.4690%	+50989000	+728117693500	+875.0663	+3.7472%	+1,063.3109	+14.9345%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
634211	178511387443307404035321335348958038819353	42	137.035	140735013617950022969738253790109316 2² × 3² × 7 × 16417 × 38447 × 2345257 × 13308167 × 28348930543	2022-10-03	13308167	28348930543	2.466e+11	34.306	63.557

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-31	Alex Kruppa	v4_computers	2000	40000		-		-	-	8.96776e-5	-	-	0.070%
2001-05-27	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.035%
2002-05-11	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	0.896%
2002-07-06	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.005	-	-	1.392%
2002-10-07	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.020%
2003-05-26	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	2.773%
2011-02-01	Jocelyn Larouche	Manual testing	2000000	2000000		-		-	-	0.044	-	-	2.386%
2013-10-26	David Campeau	i5-2500k	2080000	70720000		-		-	-	0.128	-	-	5.752%
2015-11-14	Sid & Andy	Woody	6342110	190263300	12	-		-	-	0.361	-	-	7.428%
2020-11-24	Carlos Pinho	HomeComputer	45000	1975000	6	-		-	-	0.003	-	-	1.381%
2022-10-03	masser	hwell	51000000	728120893500			178511387443307404035321335348958038819353	42	137.035	875.1	0.019	1,750	19.660%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-08-30	masser	Manual testing	5100000	219300000	2	7			-	-	0.423

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-01-12	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-15	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.015	-	-
2001-10-25	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.030	-	-
2003-10-31	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.061	-	-
2008-10-17	Sturle Sunde	buxtehude.ifi	2⁵⁸	2⁵⁹		-	-	0.061	-	-
2008-10-17	Sturle Sunde	buxtehude.ifi	2⁵⁹	2⁶⁰		-	-	0.121	-	-
2010-08-12	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.242	-	-
2015-06-06	lycorn	Manual testing	2⁶¹	2⁶²		-	-	0.484	-	-
2015-10-13	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.548	-	-
2015-10-13	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	3.096	-	-
2017-06-23	Smok_bmv	Manual testing	2⁶⁴	2⁶⁵		-	-	5.891	-	-
2017-07-20	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	11.78	-	-
2017-09-20	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	23.57	-	-
2017-09-21	Smok_bmv	Manual testing	2⁶⁷	2⁶⁸		-	-	47.13	-	-
2018-04-02	Smok_bmv	Manual testing	2⁶⁸	2⁶⁹		-	-	94.26	-	-

ECM factoring results:

Total ECM effort:	21.409 GHz-days
Estimated T-Level:	26.658

Digits	B1	Complete	FacMiss
20	11000	28.497	0.000%
25	50000	3.553	2.863%
30	250000	0.332	71.784%
35	1000000	0.025	97.529%
40	3000000	0.002	99.842%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	366	6.228
250000	25000000	149	12.68
250000	254268105	7	2.504

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-25	Chad Davis	Bayes	50000	5000000						1	0.017
2007-10-28	ANONYMOUS	minister	50000	5000000						1	0.017
2008-01-22	Steve Scott	Abit-4	50000	5000000						3	0.051
2008-09-14	Sturle Sunde	v23	50000	5000000						3	0.051
2008-11-27	Sturle Sunde	v22	50000	5000000						3	0.051
2009-03-02	Sturle Sunde	v22	50000	5000000						3	0.051
2009-04-04	Sturle Sunde	v17	50000	5000000						3	0.051
2009-07-02	Architects Cubed	m1_65	50000	5000000						3	0.051
2009-07-12	Architects Cubed	m1_68	50000	5000000						3	0.051
2009-08-31	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.051
2009-09-29	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-10-25	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.051
2009-11-13	linded	KCPB8P0-NET214	50000	5000000						3	0.051
2009-12-06	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-12-31	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-01-20	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-02-04	James Hintz	03_122109	50000	5000000						3	0.051
2010-02-23	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-03-18	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-04-05	Sturle Sunde	PRE6S32KN9Z73F9	50000	5000000						3	0.051
2010-04-24	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-05-14	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-06-04	Murphy's Law		50000	5000000						3	0.051
2010-06-27	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-07-29	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-08-25	Sturle Sunde	0020ED951D03	50000	5000000						3	0.051
2010-09-15	James Hintz	06_122109	50000	5000000						3	0.051
2010-10-02	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.051
2010-10-29	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.051
2010-11-04	Sturle Sunde	00301BB4FC73	50000	5000000						3	0.051
2010-11-24	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2010-12-07	Kamil_Górski	thefault	50000	5000000						3	0.051
2010-12-25	Sturle Sunde	PRECZC44710WB	50000	5000000						3	0.051
2011-01-12	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2011-01-25	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.051
2011-02-12	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2011-02-26	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2011-03-11	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-03-27	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-04-20	James Hintz	06_122109	50000	5000000						3	0.051
2011-05-11	Sturle Sunde	PRE0011254B6EE4	50000	5000000						3	0.051
2011-05-28	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-06-23	Palkó Tamás Attila		50000	5000000						3	0.051
2011-07-14	Lukasz Wrobel	w-l	50000	5000000						3	0.051
2011-08-13	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-10-03	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-12-05	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2012-02-03	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2012-03-17	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2012-06-06	Sturle Sunde	TOR-ST-0025	50000	5000000						3	0.051
2012-08-29	Sturle Sunde	TOR-ST-0033	50000	5000000						3	0.051
2013-02-03	Olli Heikkilä		50000	5000000						3	0.051
2013-09-30	lopper	Surface_staples	50000	5000000						3	0.051
2013-12-27	Bruce	bfc-ws	50000	5000000						3	0.051
2014-03-30	Bruce	snowflake	50000	5000000						3	0.051
2014-04-03	Bruce	snowflake	50000	5000000						3	0.051
2015-07-14	XZT	Tablet	50000	5000000						3	0.051
2015-11-19	Nacnud	Calculator	50000	5000000						3	0.051
2016-01-26	Ashguard		50000	5000000						3	0.051
2016-03-22	Obsidian	Ace	50000	5000000						3	0.051
2016-04-08	TJAOI	Manual testing	50000	5000000						17	0.289
2016-06-27	bayanne	iMac	50000	5000000						3	0.051
2016-07-08	Obsidian	Ace	50000	5000000						3	0.051
2016-07-29	Robert Martin	HomePC	50000	5000000						3	0.051
2016-08-24	ANONYMOUS	C272CE75B	50000	5000000						3	0.051
2016-09-04	Roman O. Vorobiev	Home	50000	5000000						3	0.051
2016-09-18	Obsidian	Ace	50000	5000000						3	0.051
2016-10-16	Bruce J. Wilder	VIPER	50000	5000000						3	0.051
2016-10-16	westicles	Manual testing	50000	5000000						70	1.191
2016-10-17	Oussama Kiamouche	Home	50000	5000000						3	0.051
2016-12-30	TJAOI	Manual testing	50000	5000000						79	1.344
2019-04-26	TJAOI	Manual testing	250000	25000000						27	2.297
2019-05-16	OS1	Tina	250000	25000000						3	0.255
2020-10-26	monsted	rootweiler	250000	25000000						7	0.596
2020-11-09	monsted	rootweiler	250000	25000000						7	0.596
2020-11-28	monsted	rootweiler	250000	25000000						7	0.596
2021-01-24	monsted	rootweiler	250000	25000000						7	0.596
2021-02-07	GAN	N-29	250000	25000000						7	0.596
2021-03-12	mnd9	75203	250000	25000000						7	0.596
2021-03-31	monsted	rootweiler	250000	25000000						7	0.596
2021-04-25	GAN	N-27	250000	25000000						7	0.596
2021-05-05	monsted	rootweiler	250000	25000000						7	0.596
2021-06-17	LaurV	trabi	250000	25000000						7	0.596
2021-06-19	TSRPrime	TSRLoftus	250000	25000000						7	0.596
2021-06-20	monsted	rootweiler	250000	25000000						7	0.596
2021-07-25	monsted	rootweiler	250000	25000000						7	0.596
2021-06-17	LaurV	Manual testing	250000	25000000						7	0.596
2021-10-17	Jinyuan Wang	AMD5800	250000	25000000						7	0.596
2021-12-10	voidf	T_B2	250000	25000000						7	0.596
2022-03-24	BennetF	Spezi	250000	25000000						7	0.596
2022-07-17	Oliver Kruse	Krusen-NAS	250000	254268105						7	2.504

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Ken Kriesel		62907FE74D245EA2	0.010
2015-04-11	MadPoo	Manual testing	62907FE74D245EA2	0.010

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-10-03

masser

hwell

178511387443307404035321335348958038819353

1B8B235CE13526D0

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 = 51000000, B2 = 728120893500 (P-1 stage 2)

B1 = 51000000 (P-1 stage 1)

B1 = 6342110, B2 = 190263300 (P-1 stage 2)

B1 = 6342110 (P-1 stage 1)

B1 = 2080000, B2 = 70720000 (P-1 stage 2)

B1 = 2080000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 45000, B2 = 1975000 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 45000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 40000 (P-1 stage 2)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=26.66 ~= 72-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2023-07-11T14:45:05+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