M2003191 Mersenne number exponent details

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M2003191

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is 2 ^2003191 - 1

has 603021 decimal digits

takes 0.132 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	01A925F1955F0DF3	double-checked
PRP	A35E88686DCB61FB	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷²	477.4051	70.8333%	10000000	350000000	2.7194	7.4393%	480.1245	73.0031%	2.1698%
PrimeNet	2⁵⁸	0.0192	63.7931%	8000	140000	0.0014	2.4796%	0.0206	64.6909%	0.8978%
GPU72	2⁶²	0.3067	66.1290%	8000	110000	0.0013	1.2371%	0.3080	66.5480%	0.4190%
Difference	+10	+477.0984	+4.7043%	+9992000	+349890000	+2.7181	+6.2022%	+479.8166	+6.4551%	+6.4551%

Known prime factors (1 factor, 97.5 bits, 0.00486753% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2003191	225007102354851248019601430113	30	97.506	56162168848315324904016 2⁴ × 3 × 653 × 907 × 1319 × 2657 × 563697119	2021-11-04	2657	563697119	3.092e+10	2.9282	5.4687

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.006%
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.018%
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.091%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	6000	6000		-		-	-	0.001	-	-	0.032%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	10000	10000		-		-	-	0.001	-	-	0.059%
2007-04-07T00:00:00	markr	v4_computers	100000	2000000		-		-	-	0.019	-	-	1.428%
2010-11-23T00:51:00	Jocelyn Larouche	Manual testing	200319	200319		-		-	-	0.019	-	-	0.680%
2013-10-07T20:36:00	David Campeau	Manual testing	580000	15080000		-		-	-	0.131	-	-	3.193%
2018-05-25T20:58:31	Jocelyn Larouche	low 4M	2003191	4006382	6	-		-	-	0.201	-	-	2.586%
2018-07-03T10:19:44	Jocelyn Larouche	low 4M	2003191	80127640	12	-		-	-	0.597	-	-	5.099%
2018-12-03T01:31:28	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	6.341%
2020-09-30T19:26:55	Bruno Victal	Manual testing	10000000	350000000		-		-	-	2.719	-	-	7.439%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-11-04T09:47:24	mikr	Nitron	30000000	1620000000	129	71	225007102354851248019601430113	P+1P-1	30	97.506	10.81

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.058	-	-
2009-01-02T23:26:00	Sturle Sunde	akerman.ifi	2⁶⁰	2⁶¹		-	-	0.077	-	-
2011-12-23T13:20:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.153	-	-
2013-02-05T16:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.490	-	-
2015-03-11T06:10:00	BloodIce	Manual testing	2⁶³	2⁶⁴		-	-	0.980	-	-
2015-03-11T06:10:00	BloodIce	Manual testing	2⁶⁴	2⁶⁵		-	-	1.865	-	-
2015-03-11T06:10:00	BloodIce	Manual testing	2⁶⁵	2⁶⁶		-	-	3.730	-	-
2015-03-11T06:10:00	BloodIce	Manual testing	2⁶⁶	2⁶⁷		-	-	7.461	-	-
2015-03-11T16:36:00	BloodIce	Manual testing	2⁶⁷	2⁶⁸		-	-	14.92	-	-
2015-08-23T20:39:00	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	29.84	-	-
2015-08-23T20:39:00	ramgeis	Manual testing	2⁶⁹	2⁷⁰		-	-	59.69	-	-
2015-12-18T09:42:56	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	119.4	-	-
2019-12-03T07:55:41	mikr	Manual testing	2⁷¹	2⁷²		-	-	238.7	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

23.772 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	281 / 100	2.810	5.936%
25	50000	281 / 280	1.004	36.591%

New Calculation Method

Total ECM effort:

23.772 GHz-days

Digits	B1	Complete	FacMiss
20	11000	9.065	0.012%
25	50000	0.819	44.077%
30	250000	0.050	95.080%
35	1000000	0.002	99.769%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	23.77

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-27T21:18:00	borkencode	CFF2DC1CD	50000	5000000						3	0.254
2009-09-02T15:52:00	JimBa	E5400	50000	5000000						3	0.254
2011-01-20T00:53:00	Jocelyn Larouche	Manual testing	50000	5000000						1	0.085
2011-10-11T19:58:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.254
2013-05-11T14:15:00	ANONYMOUS		50000	5000000						3	0.254
2014-12-10T08:36:00	AdolfNor	PC4	50000	5000000						3	0.254
2015-03-09T06:46:00	BloodIce	Mjolnir4	50000	5000000						92	7.783
2015-03-13T09:38:00	BloodIce	Mjolnir4	50000	5000000						173	14.64

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	01A925F1955F0DF3	0.132
1999-05-23T00:00:00	carlo_baffa	v4_computers	01A925F1955F0DF3	0.132
2015-10-29T03:39:37	MadPoo	Manual testing	01A925F1955F0DF3	0.132

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-11-04T10:31:52

SRJ2877

LTOS

225007102354851248019601430113

A35E88686DCB61FB

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 = 30000000, B2 = 1620000000 (P+1 stage 2)

B1 = 30000000 (P+1 stage 1)

B1 = 10000000, B2 = 350000000 (P-1 stage 2)

B1 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 2003191, B2 = 80127640 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 2003191, B2 = 4006382 (P-1 stage 2)

B1 = 2003191 (P-1 stage 1)

B1 = 580000, B2 = 15080000 (P-1 stage 2)

B1 = 580000 (P-1 stage 1)

B1 = 100000, B2 = 2000000 (P-1 stage 2)

B1 = 200319 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 6000 (P-1 stage 1)

B1 = 4000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-11-04T10:31:52+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