M1441361 Mersenne number exponent details

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M1441361

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is 2 ^1441361 - 1

has 433893 decimal digits

takes 0.055 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	34D9C2FD7F334728	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	20.6152	68.6567%	2000000	60000000	0.2857	7.2245%	20.9008	70.9211%	2.2644%
PrimeNet	2⁵⁶	0.0067	62.5000%	6500	110000	0.0007	2.7778%	0.0073	63.5417%	1.0417%
GPU72	2⁶⁰	0.1066	65.0000%	6000	90000	0.0006	1.3554%	0.1071	65.4744%	0.4744%
Difference	+7	+20.5086	+3.6567%	+1994000	+59910000	+0.2851	+5.8691%	+20.7937	+5.4467%	+5.4467%

Known prime factors (1 factor, 71.7 bits, 0.00497649% 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
1441361	3914196168889622777423	22	71.729	1357812570511351 509 × 769 × 3468931331	2015-10-05	769	3468931331	333.91	10.463	19.542

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.838%
2010-05-17T14:39:00	Rob_Dee	twopc	100000	200000		-		-	-	0.006	-	-	1.215%
2010-05-18T14:46:00	Rob_Dee	twopc	200000	1000000		-		-	-	0.013	-	-	2.331%
2010-05-19T19:13:00	Rob_Dee	twopc	200000	2000000		-		-	-	0.017	-	-	2.817%
2010-05-20T16:31:00	Rob_Dee	twopc	200000	3000000		-		-	-	0.020	-	-	3.108%
2010-05-21T15:50:00	Rob_Dee	twopc	200000	4000000		-		-	-	0.023	-	-	3.318%
2010-05-22T16:10:00	Rob_Dee	twopc	200000	5000000		-		-	-	0.026	-	-	3.482%
2014-11-14T01:20:00	Jocelyn Larouche	Manual testing	244530	244530		-		-	-	0.014	-	-	1.385%
2015-01-27T21:58:00	Jocelyn Larouche	Manual testing	325469	325469		-		-	-	0.018	-	-	1.589%
2015-01-30T21:42:00	Jocelyn Larouche	Manual testing	358015	358015		-		-	-	0.020	-	-	1.660%
2015-02-13T18:00:00	Jocelyn Larouche	Manual testing	393816	393816		-		-	-	0.022	-	-	1.733%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	476516	476516		-		-	-	0.026	-	-	1.885%
2015-03-03T20:46:00	Jocelyn Larouche	Manual testing	524167	524167		-		-	-	0.029	-	-	1.964%
2015-03-10T07:55:00	Jocelyn Larouche	Manual testing	576583	576583		-		-	-	0.032	-	-	2.045%
2015-04-08T16:58:00	Jocelyn Larouche	Manual testing	767431	767431		-		-	-	0.042	-	-	2.298%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	928591	928591		-		-	-	0.051	-	-	2.475%
2015-05-03T21:49:00	alpertron	Manual testing	2000000	60000000		-		-	-	0.286	-	-	7.224%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-
2010-05-11T14:40:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.107	-	-
2011-07-17T18:55:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.107	-	-
2015-03-22T20:54:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.362	-	-
2015-03-22T22:51:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.592	-	-
2015-09-15T08:33:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	5.185	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.502 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.502 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	11.82
50000	5000000	3914196168889622777423	1	0.047
250000	35000000		50	13.63

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-03-07T20:03:00	Sturle Sunde	lara	50000	5000000						3	0.142
2009-03-05T16:25:00	Sturle Sunde	FLB-ST-0035	50000	5000000						3	0.142
2009-10-24T06:36:00	JimBa	NASsrvr	50000	5000000						3	0.142
2011-05-08T02:20:00	James Hintz	ryan	50000	5000000						3	0.142
2012-04-11T04:56:00	driveByUpgrades		50000	5000000						3	0.142
2013-05-03T21:24:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2013-11-21T19:17:00	arnaud	SPR14	50000	5000000						3	0.142
2014-07-15T09:23:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-03-17T15:28:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-10-05T06:49:37	Chang Chia-Tche	exbpc13	50000	5000000	3914196168889622777423	71.729	1	2		1	0.047
2019-03-15T12:29:12	TJAOI	Manual testing	50000	5000000						223	10.55
2022-01-25T11:43:31	TJAOI	Manual testing	250000	35000000						50	13.63

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	34D9C2FD7F334728	0.055
2015-07-19T16:38:00	MadPoo	Manual testing	34D9C2FD7F334728	0.055

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:29:01

alpertron

Manual testing

3914196168889622777423

C100337F031926__

2017-10-18T06:52:06

Oliver Kruse

Threadripper

3914196168889622777423

C100337F031926__

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

B1 = 2000000 (P-1 stage 1)

B1 = 928591 (P-1 stage 1)

B1 = 767431 (P-1 stage 1)

B1 = 576583 (P-1 stage 1)

B1 = 524167 (P-1 stage 1)

B1 = 476516 (P-1 stage 1)

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

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

B1 = 393816 (P-1 stage 1)

B1 = 358015 (P-1 stage 1)

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

B1 = 325469 (P-1 stage 1)

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

B1 = 244530 (P-1 stage 1)

B1 = 200000, B2 = 1000000 (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)

10¹

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10¹

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TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

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2¹⁰⁰

Last modified: 2022-01-25T11:43:31+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