M1 614 289 Mersenne number exponent details

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M1614289

<<<

>>>

is 2 ^1614289 - 1

has 485950 decimal digits

takes 0.072 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	B26EA055B0C755F9	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	36.9233	69.1176%	25000000	322351801200	1,139.0030	19.9527%	1,175.9263	75.2795%
Target	2⁶¹	0.1903	65.5738%	6500	300000	0.0015	1.0584%	0.1917	65.9381%
Difference	+7	+36.7330	+3.5439%	+24993500	+322351501200	+1,139.0015	+18.8943%	+1,175.7346	+9.3414%

Known prime factors (1 factor, 128.4 bits, 0.00795550% 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
1614289	456766322801737399044944446569067288633	39	128.425	141476006713090840315750292100444 2² × 3² × 179 × 2813719 × 3955691 × 6810203 × 289643723	2022-11-04	6810203	289643723	8.903e+10	1.4391	1.9089

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-11-18	BigBrother	Winston	1000000	20000000		-		-	-	0.132	-	-	5.174%
2017-07-18	Jocelyn Larouche	low 4M	1200000	12000000	12	-		-	-	0.116	-	-	4.749%
2017-08-07	Jocelyn Larouche	low 4M	2000000	20000000	12	-		-	-	0.193	-	-	5.489%
2018-02-03	VictordeHollander	Manual testing	10000000	200000000	12	-		-	-	1.318	-	-	9.066%
2022-11-04	Naegi Makoto	5950X	25000000	322351801200			456766322801737399044944446569067288633	39	128.425	1,139	0.144	2,278	19.953%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-05-18	Team_Inspector	Purple	1000000	50000000	2	7			-	-	0.268

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-07-21	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.071	-	-
2010-05-04	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.095	-	-
2016-02-23	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.190	-	-
2010-07-17	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.989	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.608	-	-
2015-04-26	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.216	-	-
2015-04-27	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.315	-	-
2015-10-11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.629	-	-
2017-11-24	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	9.258	-	-
2019-09-13	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	18.52	-	-

ECM factoring results:

Total ECM effort:	29.906 GHz-days
Estimated T-Level:	25.672

Digits	B1	Complete	FacMiss
20	11000	14.869	0.000%
25	50000	1.637	19.455%
30	250000	0.134	87.424%
35	1000000	0.009	99.106%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	15.71
250000	40000000		41	14.19

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-04-10	Steve Scott	Celeron	50000	5000000						3	0.168
2009-05-27	KAMCOBILL	PC18	50000	5000000						3	0.168
2010-04-14	John Tolly	mac	50000	5000000						3	0.168
2011-08-28	S36049	Wolle5	50000	5000000						3	0.168
2013-03-11	Jacques MOLNE	Old_faithfull	50000	5000000						3	0.168
2013-11-04	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2014-05-08	mikr	MSI	50000	5000000						12	0.673
2016-03-22	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2016-05-03	Bruce	DESK3	50000	5000000						3	0.168
2016-07-27	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2016-09-25	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2016-11-21	Bruce	DESK3	50000	5000000						3	0.168
2017-01-12	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2017-04-26	ANONYMOUS	Worker	50000	5000000						3	0.168
2017-09-08	VictordeHollander	Manual testing	50000	5000000						229	12.85
2022-08-23	TJAOI	Manual testing	250000	40000000						41	14.19

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Kevin Quiggle		B26EA055B0C755F9	0.072
1999-07-27	ANONYMOUS	v4_computers	B26EA055B0C755F9	0.072
2015-07-06	MadPoo	Manual testing	B26EA055B0C755F9	0.072

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-11-04

Naegi Makoto

i5_T

456766322801737399044944446569067288633

A0AF095A10913FD6

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 = 25000000, B2 = 322351801200 (P-1 stage 2)

B1 = 25000000 (P-1 stage 1)

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

B1 = 10000000 (P-1 stage 1)

B1 = 2000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1200000, B2 = 12000000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10⁵

10⁶

10⁷

10⁸

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

this exponent TF target: 61

TF double-checked to: 67.9

ECM T-Level=25.67 ~= 69-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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