M386 731 Mersenne number exponent details

is 2 ³⁸⁶⁷³¹ - 1

has 116418 decimal digits

takes 0.004 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	2⁶⁸	154.1249	72.0588%	73000000	2103141080040	1,611.6842	21.9143%	1,765.8091	78.1819%
Target	2⁴⁴	0.0000	56.8182%	7000	1600000	0.0013	12.7894%	0.0013	62.3409%
Difference	+24	+154.1249	+15.2406%	+72993000	+2103139480040	+1,611.6829	+9.1249%	+1,765.8078	+15.8411%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
386731	11746748923486868639789909944341992329681	41	133.109	15187234697356649246879497563347640 2³ × 3² × 5 × 41 × 59 × 557 × 1033 × 170029 × 10017853 × 17794556293	2023-07-31	10017853	17794556293	4.009e+11	13.761	25.454

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-10	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.001	-	-	1.260%
2002-06-15	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.003	-	-	1.462%
2002-08-24	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.006	-	-	2.114%
2012-07-25	alpertron	Manual testing	10000000	200000000		-		-	-	0.286	-	-	7.957%
2017-01-13	mikr	S052	60000000	3000000000	12	-		-	-	3.095	-	-	12.559%
2023-02-06	Jocelyn Larouche	Manual testing	1000000	28509731250		-		-	-	21.85	-	-	11.279%
2023-07-20	Joss	Joss	1000000	68245727550		-		-	-	52.28	-	-	12.165%
2023-07-31	JacobZ	PM1Server	73000000	2103141080040			11746748923486868639789909944341992329681	41	133.109	1,612	0.007	3,223	21.914%

P+1 Factoring results:

date	userid	compid	b1	b2	start		digits	bits*	ghz-days
2022-12-26	masser	Manual testing	20000000	620000000	170	59	-	-	0.878
2022-12-27	masser	Manual testing	20000000	640000000	2	7	-	-	0.893
2023-01-04	masser	Manual testing	20000000	640000000	6	5	-	-	0.893

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-12-01	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-
2000-04-27	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.006	-	-
2022-03-07	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.006	-	-
2001-03-17	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.025	-	-
2002-01-28	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.050	-	-
2004-01-18	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.099	-	-
2009-01-06	Sturle Sunde	ghibu.ifi	2⁵⁸	2⁵⁹		-	-	0.099	-	-
2009-01-09	Sturle Sunde	golli.ifi	2⁵⁹	2⁶⁰		-	-	0.199	-	-
2012-11-27	dbaugh	Manual testing	2⁶⁰	2⁶¹		-	-	0.397	-	-
2012-12-01	dbaugh	Manual testing	2⁶¹	2⁶²		-	-	0.794	-	-
2015-11-25	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	2.538	-	-
2015-11-25	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	5.077	-	-
2018-02-01	BloodERazor	Manual testing	2⁶⁴	2⁶⁵		-	-	9.66	-	-
2019-05-21	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	19.32	-	-
2022-03-13	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	38.65	-	-
2022-12-04	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	77.29	-	-

ECM factoring results:

Total ECM effort:	33.701 GHz-days
Estimated T-Level:	29.863

Digits	B1	Complete	FacMiss
20	11000	63.951	0.000%
25	50000	9.236	0.010%
30	250000	0.973	37.808%
35	1000000	0.080	92.311%
40	3000000	0.005	99.466%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	2.944
250000	25000000		585	30.76

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-13	George Woltman	D_P4Debug	50000	5000000						1	0.011
2007-08-30	Team_Bundu	bundu1	50000	5000000						1	0.011
2007-09-27	ANONYMOUS	minister	50000	5000000						1	0.011
2008-01-02	Steve Scott		50000	5000000						1	0.011
2008-01-02	Steve Scott		50000	5000000						1	0.011
2008-01-02	Steve Scott		50000	5000000						1	0.011
2008-01-02	Steve Scott	Abit	50000	5000000						1	0.011
2008-03-17	Scott Kurowski	HomeOffice	50000	5000000						3	0.032
2008-09-15	Sturle Sunde	v23	50000	5000000						3	0.032
2008-10-29	Jayson King	atlas	50000	5000000						3	0.032
2008-12-08	Jayson King	atlas	50000	5000000						3	0.032
2009-01-30	Dalos Lee	dalosdesk	50000	5000000						3	0.032
2009-03-05	Sturle Sunde	v21	50000	5000000						3	0.032
2009-03-31	Ryan Schulz	T7400	50000	5000000						3	0.032
2009-05-28	linded	KCPB8P0-NET214	50000	5000000						3	0.032
2009-07-02	Architects Cubed	m1_58	50000	5000000						3	0.032
2009-07-09	Architects Cubed	m1_44	50000	5000000						3	0.032
2009-07-26	Architects Cubed	m1_13	50000	5000000						3	0.032
2009-08-23	JimBa	CIT3srvr	50000	5000000						3	0.032
2009-09-15	David Bessell	L301	50000	5000000						3	0.032
2009-10-01	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2009-10-29	alpertron	core2quad	50000	5000000						3	0.032
2009-11-09	David Bessell	G810	50000	5000000						3	0.032
2009-11-22	David Bessell	G810	50000	5000000						3	0.032
2009-12-06	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2009-12-19	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-01-03	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-01-15	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-01-25	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-02-03	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-02-04	James Hintz	18_012210	50000	5000000						3	0.032
2010-02-12	Sturle Sunde	TOR-ST-0020	50000	5000000						3	0.032
2010-02-27	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-03-12	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-03-23	Sturle Sunde	TOR-ST-0017	50000	5000000						3	0.032
2010-04-03	David Bessell	L301	50000	5000000						3	0.032
2010-04-14	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.032
2010-04-25	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-05-06	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-05-18	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-05-30	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-06-13	Sturle Sunde	000461A92481	50000	5000000						3	0.032
2010-06-27	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-07-17	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-08-03	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-08-20	Sturle Sunde	PRE6S32KN9Z73PR	50000	5000000						3	0.032
2010-09-01	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-09-11	Sturle Sunde	TOR-ST-0027	50000	5000000						3	0.032
2010-09-22	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-10-03	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.032
2010-10-13	Sturle Sunde	0020ED7F6D0F	50000	5000000						3	0.032
2010-10-22	sannerud.com	Jim2010	50000	5000000						3	0.032
2010-11-01	josibo	Ziben	50000	5000000						3	0.032
2010-11-10	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-12-03	sannerud.com	Jim2010	50000	5000000						3	0.032
2010-12-10	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-12-20	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-01-01	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-01-11	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-01-19	Damian Silvestre	PcMa	50000	5000000						3	0.032
2011-02-07	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-02-20	Carsten Kossendey	mother	50000	5000000						10	0.105
2011-03-02	James Hintz	06_122109	50000	5000000						3	0.032
2011-03-15	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-03-18	Sturle Sunde	PRE6S33KN9ZE3B5	50000	5000000						3	0.032
2011-03-26	James Hintz	06_122109	50000	5000000						3	0.032
2011-04-05	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-04-19	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-05-03	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-05-14	Sturle Sunde	PRE0011254B6EE4	50000	5000000						3	0.032
2011-05-24	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-06-03	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-06-14	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.032
2011-07-01	Carsten Kossendey	mother	50000	5000000						3	0.032
2011-07-17	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-08-04	Lukasz Wrobel	w-l	50000	5000000						3	0.032
2011-08-22	Lukasz Wrobel	w-l	50000	5000000						3	0.032
2011-09-28	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2011-11-22	Carsten Kossendey	mother	50000	5000000						10	0.105
2012-02-23	James Hintz	06_122109	50000	5000000						3	0.032
2012-03-18	Sturle Sunde	TOR-ST-0033	50000	5000000						3	0.032
2012-05-11	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.032
2012-05-11	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.032
2012-05-31	MadPoo	IntLAVH03	50000	5000000						3	0.032
2012-06-04	MadPoo	IntLAVH03	50000	5000000						3	0.032
2013-01-14	HVer	dell	50000	5000000						3	0.032
2013-02-03	Le Comte	S761	50000	5000000						22	0.231
2013-06-21	Sergiosi	Manual testing	250000	25000000						194	10.20
2019-04-12	alex	aws-m5dmetal	250000	25000000						391	20.56

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Marc Honey		E446162483DB6295	0.004
2002-11-09	ANONYMOUS	v4_computers	E446162483DB6295	0.004

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-08-06

JacobZ

MServer

11746748923486868639789909944341992329681

60B1C9BA9497B620

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 = 73000000, B2 = 2103141080040 (P-1 stage 2)

B1 = 1000000, B2 = 68245727550 (P-1 stage 2)

B1 = 1000000, B2 = 28509731250 (P-1 stage 2)

B1 = 60000000, B2 = 3000000000 (P-1 stage 2)

B1 = 73000000 (P-1 stage 1)

B1 = 60000000 (P-1 stage 1)

B1 = 10000000, B2 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

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

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

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵³

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=29.86 ~= 83-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2023-08-06T22:18:26+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