M1 457 791 Mersenne number exponent details

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M1457791

<<<

>>>

is 2 ^1457791 - 1

has 438839 decimal digits

takes 0.056 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	9779439E883EF6E8	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	40.8871	69.1176%	1457791	17763296460	53.6551	12.7156%	94.5422	73.0445%
Target	2⁶⁰	0.1054	65.0000%	6500	450000	0.0017	1.3981%	0.1071	65.4893%
Difference	+8	+40.7818	+4.1176%	+1451291	+17762846460	+53.6534	+11.3175%	+94.4352	+7.5552%

Known prime factors (1 factor, 98.4 bits, 0.00674778% 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
1457791	409131556834701105370950956281	30	98.368	140325861812393239281540 2² × 3³ × 5 × 35323 × 705989 × 10420497233	2023-06-25	705989	10420497233	5.147e+10	31.468	58.704

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.717%
2010-09-10	Rob_Dee	twopc	100000	200000		-		-	-	0.006	-	-	1.064%
2010-09-11	Rob_Dee	twopc	200000	300000		-		-	-	0.011	-	-	1.340%
2010-09-12	Rob_Dee	twopc	200000	1000000		-		-	-	0.013	-	-	2.078%
2010-09-13	Rob_Dee	twopc	200000	2000000		-		-	-	0.017	-	-	2.521%
2010-09-14	Rob_Dee	twopc	200000	3000000		-		-	-	0.020	-	-	2.786%
2010-09-15	Rob_Dee	twopc	200000	4000000		-		-	-	0.023	-	-	2.977%
2010-09-16	Rob_Dee	twopc	200000	5000000		-		-	-	0.026	-	-	3.127%
2014-11-19	Jocelyn Larouche	Manual testing	244028	244028		-		-	-	0.014	-	-	1.220%
2015-01-26	Jocelyn Larouche	Manual testing	295273	295273		-		-	-	0.016	-	-	1.341%
2015-01-28	Jocelyn Larouche	Manual testing	324800	324800		-		-	-	0.018	-	-	1.404%
2015-02-02	Jocelyn Larouche	Manual testing	393008	393008		-		-	-	0.022	-	-	1.536%
2015-02-16	alpertron	Manual testing	2000000	60000000		-		-	-	0.286	-	-	6.641%
2016-08-22	Bruno Victal	5820K-factoring	2500000	62500000	12	-		-	-	0.319	-	-	6.812%
2016-08-27	Bruno Victal	Manual testing	2500000	62500000	12	-		-	-	0.319	-	-	6.812%
2018-06-05	Jocelyn Larouche	low 4M	1457791	145779100	12	-		-	-	0.516	-	-	7.402%
2018-10-15	Jocelyn Larouche	low 4M	1457791	160357010	12	-		-	-	0.560	-	-	7.505%
2022-12-22	Jocelyn Larouche	Manual testing	1457791	1222401180		-		-	-	3.763	-	-	9.733%
2022-12-23	Kirill Frolov	shodan1	1750000	3810132690		-		-	-	11.58	-	-	11.213%
2023-06-25	Joss	Joss	1457791	17763296460			409131556834701105370950956281	30	98.368	53.66	0.111	107.3	12.716%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-13	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-21	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.079	-	-
2010-05-08	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.105	-	-
2016-02-23	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.211	-	-
2011-04-05	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.095	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.673	-	-
2015-03-28	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.347	-	-
2015-03-28	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.563	-	-
2015-09-18	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	5.126	-	-
2018-03-19	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	10.25	-	-
2020-02-14	Gordon Spence	Manual testing	2⁶⁷	2⁶⁸		-	-	20.50	-	-

ECM factoring results:

Total ECM effort:	25.556 GHz-days
Estimated T-Level:	25.704

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.89
250000	35000000		50	13.66

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-05	Scott Kurowski	v5_node.1	50000	5000000						1	0.047
2008-12-31	Xyzzy	Xyzzy-YV	50000	5000000						3	0.142
2009-10-01	Piepen	T41-2000	50000	5000000						3	0.142
2010-04-28	James Hintz	terri_castor	50000	5000000						3	0.142
2011-07-25	S36049	Wolle5	50000	5000000						3	0.142
2012-11-24	Donna Noble	PH2x6	50000	5000000						3	0.142
2013-09-11	OS1	L3	50000	5000000						3	0.142
2014-02-17	Bruce	snowflake	50000	5000000						3	0.142
2014-11-11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-05-13	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-11-17	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2016-02-25	Bruce	DESK3	50000	5000000						3	0.142
2016-03-29	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2016-05-02	Bruce	DESK3	50000	5000000						3	0.142
2016-07-08	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2016-09-09	Bruce	test	50000	5000000						3	0.142
2016-11-01	Bruce	DESK3	50000	5000000						3	0.142
2016-12-21	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2017-02-19	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2017-08-06	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2017-12-05	Bruce	DESK3	50000	5000000						3	0.142
2018-01-26	Bruce	DESK3	50000	5000000						3	0.142
2018-03-24	Lelikoid	QH	50000	5000000						3	0.142
2019-03-15	TJAOI	Manual testing	50000	5000000						184	8.718
2022-02-03	TJAOI	Manual testing	250000	35000000						50	13.66

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Barrett Davis		9779439E883EF6E8	0.056
1999-01-10	Stephen Wood	v4_computers	9779439E883EF6E8	0.056
2015-06-27	MadPoo	Manual testing	9779439E883EF6E8	0.056

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-06-27

Naegi Makoto

5950X

409131556834701105370950956281

BC656FD6D9342790

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 = 1457791, B2 = 17763296460 (P-1 stage 2)

B1 = 1750000, B2 = 3810132690 (P-1 stage 2)

B1 = 1457791, B2 = 1222401180 (P-1 stage 2)

B1 = 1457791, B2 = 160357010 (P-1 stage 2)

B1 = 1457791, B2 = 145779100 (P-1 stage 2)

B1 = 2500000, B2 = 62500000 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 1750000 (P-1 stage 1)

B1 = 1457791 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 200000, B2 = 4000000 (P-1 stage 2)

B1 = 393008 (P-1 stage 1)

B1 = 200000, B2 = 3000000 (P-1 stage 2)

B1 = 324800 (P-1 stage 1)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 295273 (P-1 stage 1)

B1 = 244028 (P-1 stage 1)

B1 = 200000, B2 = 1000000 (P-1 stage 2)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

this exponent TF target: 60

TF double-checked to: 67.9

ECM T-Level=25.7 ~= 69-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

JSON version of this page

Last modified: 2023-10-02T12:12:48+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