M3659501 Mersenne number exponent details

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M3659501

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>>>

is 2 ^3659501 - 1

has 1101620 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	BA6EEDE9F473E8C5	double-checked
PRP	56455701A272609A	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	65.2960	68.5714%	30000000	600000000	9.2981	10.3769%	74.5941	71.8327%	3.2613%
PrimeNet	2⁶⁰	0.0420	63.3333%	16000	320000	0.0050	3.0778%	0.0469	64.4618%	1.1285%
GPU72	2⁶⁴	0.9726	65.6250%	22000	400000	0.0065	2.0372%	0.9791	66.3253%	0.7003%
Difference	+6	+64.3233	+2.9464%	+29978000	+599600000	+9.2916	+8.3397%	+73.6150	+5.5075%	+5.5075%

Known prime factors (1 factor, 70.2 bits, 0.00191932% 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
3659501	1391864457723466465807	22	70.238	190171345454403 3 × 63390448484801	2020-12-19	3	63390448484801	80.614	525,963	982,352

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-08T05:50:00	Carsten Kossendey	leela	20000	250000		-		-	-	0.005	-	-	0.713%
2012-02-02T21:19:00	Squeeky_Squirrel	P4_2600	90000	1642500		-		-	-	0.027	-	-	1.878%
2016-06-18T21:49:05	Jocelyn Larouche	Manual testing	108000	3285000	6	-		-	-	0.043	-	-	2.306%
2016-12-29T20:13:49	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.775%
2017-01-30T01:30:55	Jocelyn Larouche	low 4M	167520	167520		-		-	-	0.026	-	-	0.898%
2017-03-07T20:00:43	Jocelyn Larouche	low 4M	241228	2412280	6	-		-	-	0.055	-	-	2.478%
2020-09-23T16:56:47	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.377%
2022-03-04T04:19:00	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.621%
2022-03-22T11:09:23	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.663%
2022-05-25T14:14:12	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.364%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-07-29T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-08-09T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-09-06T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-09-13T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-09-27T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-10-18T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-10-29T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
1998-11-14T00:00:00	Bjørn Skog	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-09T16:55:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-07T16:27:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.084	-	-
2012-06-05T02:31:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.436	-	-
2016-02-23T16:29:35	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.268	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.536	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.021	-	-
2015-10-21T10:28:03	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.042	-	-
2016-12-30T23:58:45	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.084	-	-
2019-01-07T14:44:09	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.168	-	-
2020-11-10T01:26:29	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.34	-	-
2020-11-21T07:50:15	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.67	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.272 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

New Calculation Method

Total ECM effort:	3.272 GHz-days
Estimated T-Level:	1.100

Digits	B1	Complete	FacMiss
20	11000	0.846	42.906%
25	50000	0.078	92.469%
30	250000	0.005	99.507%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		16	2.379
50000	5000000	1391864457723466465807	6	0.892

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-17T05:46:00	NeedGem Liou	OldServer	50000	5000000						3	0.446
2012-06-17T00:36:00	S36049	Wolle5	50000	5000000						3	0.446
2015-10-04T09:58:39	driveByUpgrades	Build_4	50000	5000000						3	0.446
2017-05-24T22:13:42	Lelikoid	QH	50000	5000000						3	0.446
2020-12-19T03:53:49	axn	Manual testing	50000	5000000	1391864457723466465807	70.238	6	2	2477876738627735	6	0.892
2020-12-19T03:53:49	axn	Manual testing	50000	5000000						4	0.595

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-09-06T00:00:00	Bjørn Skog	v4_computers	BA6EEDE9F473E8C5	0.384
1998-09-13T00:00:00	Bjørn Skog	v4_computers	BA6EEDE9F473E8C5	0.384
1998-09-27T00:00:00	Bjørn Skog	v4_computers	BA6EEDE9F473E8C5	0.384
1998-10-18T00:00:00	Bjørn Skog	v4_computers	BA6EEDE9F473E8C5	0.384
1998-10-29T00:00:00	Bjørn Skog	v4_computers	BA6EEDE9F473E8C5	0.384
1998-11-14T00:00:00	Bjørn Skog	v4_computers	BA6EEDE9F473E8C5	0.384
1999-09-30T00:00:00	ANONYMOUS	v4_computers	BA6EEDE9F473E8C5	0.384

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-12-19T16:40:25

Niels_Mache_Nextcloud

conf4-a

1391864457723466465807

56455701A272609A

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 = 100000, B2 = 130364850 (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 = 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 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

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TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-25T14:14:12+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