M3655937 Mersenne number exponent details

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M3655937

<<<

>>>

is 2 ^3655937 - 1

has 1100547 decimal digits

takes 0.384 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	-unknown-	-unknown-
PRP	AE1B8B0AAB8ED2BA	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	2⁷⁰	65.3596	68.5714%	30000000	600000000	9.2981	10.3761%	74.6577	71.8325%	3.2610%
PrimeNet	2⁶⁰	0.0420	63.3333%	16000	320000	0.0050	3.0773%	0.0470	64.4617%	1.1283%
GPU72	2⁶⁴	0.9736	65.6250%	22000	400000	0.0065	2.0368%	0.9801	66.3252%	0.7002%
Difference	+6	+64.3860	+2.9464%	+29978000	+599600000	+9.2916	+8.3392%	+73.6777	+5.5073%	+5.5073%

Known prime factors (1 factor, 77.4 bits, 0.00211640% 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
3655937	195859029830217964992401	24	77.374	26786433933382600 2³ × 5² × 179 × 748224411547	2021-09-06	179	748224411547	9,097.0	6,208.2	11,595

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T17:49:00	Carsten Kossendey	leela	20000	250000		-		-	-	0.005	-	-	0.713%
2012-01-31T17:57:00	Squeeky_Squirrel	P4_2600	90000	1642500		-		-	-	0.027	-	-	1.877%
2016-06-14T05:02:32	Jocelyn Larouche	Manual testing	108000	3285000	6	-		-	-	0.043	-	-	2.306%
2016-12-29T20:13:47	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.775%
2017-01-30T01:30:53	Jocelyn Larouche	low 4M	167520	167520		-		-	-	0.026	-	-	0.897%
2017-03-07T20:00:42	Jocelyn Larouche	low 4M	241228	2412280	6	-		-	-	0.055	-	-	2.478%
2017-03-11T14:04:11	Squeeky_Squirrel	P4_2600	230000	6785000	12	-		-	-	0.089	-	-	3.122%
2020-09-15T02:03:43	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.376%
2022-03-04T04:19:04	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.621%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-01T00:00:00	Hans-Martin Anger	v4_computers	2¹	2⁵⁹		-	-	0.021	-	-
2016-02-23T16:29:35	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.021	-	-
2009-03-09T16:55:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-11T17:52:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.084	-	-
2012-06-05T02:30:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.437	-	-
2016-02-23T16:29:35	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.269	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.537	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.022	-	-
2015-10-20T08:54:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.044	-	-
2016-12-30T23:58:44	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.088	-	-
2019-01-21T12:54:03	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.176	-	-
2020-11-09T01:39:41	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.35	-	-
2020-11-19T18:07:54	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.70	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.420 GHz-days
Estimated T-Level:	1.150

Digits	B1	Curves	Complete	FacMiss
20	11000	23 / 100	0.230	79.361%
25	50000	23 / 280	0.082	92.100%

New Calculation Method

Total ECM effort:	3.420 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.742	47.619%
25	50000	0.067	93.514%
30	250000	0.004	99.588%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.271
50000	5000000	195859029830217964992401	1	0.149

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-01T07:44:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.446
2012-06-13T23:18:00	Lukasz Wrobel	i-5	50000	5000000						3	0.446
2015-09-25T03:46:33	Richard Kint	Desktop	50000	5000000						3	0.446
2017-05-19T22:03:24	nokno	leo235	50000	5000000						3	0.446
2020-12-04T08:21:56	axn	Manual testing	50000	5000000						10	1.487
2021-09-06T21:26:44	daveward2005	Dave2	50000	5000000	195859029830217964992401	77.374	1	2	2027246397419881	1	0.149

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-14T00:00:00	ANONYMOUS	v4_computers	D24D83C44AE8DA__	0.384

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-09-12T16:01:40

Yizhe Huang

clb2

195859029830217964992401

AE1B8B0AAB8ED2BA

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 = 600000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

B1 = 230000, B2 = 6785000 (P-1 stage 2)

B1 = 241228, B2 = 2412280 (P-1 stage 2)

B1 = 108000, B2 = 3285000 (P-1 stage 2)

B1 = 241228 (P-1 stage 1)

B1 = 230000 (P-1 stage 1)

B1 = 90000, B2 = 1642500 (P-1 stage 2)

B1 = 167520 (P-1 stage 1)

B1 = 129600 (P-1 stage 1)

B1 = 108000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 250000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-04T04:19:04+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