M3639409 Mersenne number exponent details

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M3639409

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>>>

is 2 ^3639409 - 1

has 1095572 decimal digits

takes 0.382 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

1 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	1D3CBED0AE2C81__	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	2⁶⁹	32.8039	68.1159%	30000000	1000000000	12.6170	11.8584%	45.4209	71.8969%	3.7809%
PrimeNet	2⁶⁰	0.0422	63.3333%	16000	320000	0.0050	3.0748%	0.0472	64.4608%	1.1274%
GPU72	2⁶⁴	0.9780	65.6250%	22000	400000	0.0065	2.0352%	0.9845	66.3246%	0.6996%
Difference	+5	+31.8259	+2.4909%	+29978000	+999600000	+12.6105	+9.8233%	+44.4364	+5.5723%	+5.5723%

Known prime factors (1 factor, 70.1 bits, 0.00192660% 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
3639409	1280158113937910436497	22	70.117	175874450211272 2³ × 8929 × 2462124121	2021-08-20	8929	2462124121	84.884	20.430	38.155

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T11:20:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.825%
2012-01-24T10:46:00	Squeeky_Squirrel	P4_2600	90000	1620000		-		-	-	0.026	-	-	2.114%
2016-06-08T14:59:30	Jocelyn Larouche	Manual testing	108000	3240000	6	-		-	-	0.042	-	-	2.585%
2016-12-28T01:46:02	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.890%
2017-01-30T01:30:50	Jocelyn Larouche	low 4M	167520	167520		-		-	-	0.026	-	-	1.026%
2017-02-04T18:43:01	Jocelyn Larouche	low 4M	201024	201024		-		-	-	0.031	-	-	1.131%
2017-03-02T20:51:37	Jocelyn Larouche	low 4M	241228	2412280	6	-		-	-	0.055	-	-	2.767%
2020-07-25T02:09:14	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	11.090%
2020-08-19T08:25:57	axn	Manual testing	30000000	1000000000	12	-		-	-	12.62	-	-	11.858%
2022-03-04T04:19:11	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.717%
2022-03-22T11:09:26	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.765%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-07-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-10T16:49:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-17T05:33:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.084	-	-
2012-06-20T01:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.439	-	-
2016-02-23T16:29:35	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.270	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.539	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.027	-	-
2015-10-18T15:17:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.053	-	-
2016-12-26T04:42:24	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.107	-	-
2018-08-06T14:04:58	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.213	-	-
2020-11-06T07:02:35	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.43	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.011 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	4.011 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.268
50000	5000000	1280158113937910436497	5	0.743

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-29T03:57:00	Matt	Dell	50000	5000000						3	0.446
2012-05-10T10:34:00	sannerud.com	Jens2010	50000	5000000						3	0.446
2015-09-08T06:30:00	driveByUpgrades	Build_4	50000	5000000						3	0.446
2017-05-07T23:46:37	bayanne	iMac	50000	5000000						3	0.446
2020-11-21T04:39:42	axn	Manual testing	50000	5000000						3	0.446
2021-07-04T02:02:41	Jonathan Webb	do-primes-2	50000	5000000						7	1.040
2021-08-20T14:56:26	daveward2005	Dave2	50000	5000000	1280158113937910436497	70.117	5	2	916898731666499	5	0.743

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-10-07T00:00:00	ANONYMOUS	v4_computers	550B85BE7FEF68__	0.382

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-22T19:04:11

GURA LOVE

1280158113937910436497

1D3CBED0AE2C81__

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 = 1000000000 (P-1 stage 2)

B1 = 30000000, B2 = 600000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

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

B1 = 108000, B2 = 3240000 (P-1 stage 2)

B1 = 241228 (P-1 stage 1)

B1 = 201024 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (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 = 245000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-22T11:09:26+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