M3689617 Mersenne number exponent details

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M3689617

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>>>

is 2 ^3689617 - 1

has 1110686 decimal digits

takes 0.388 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	CC11624ACBF09717	double-checked
PRP	808FE3B71D6237BF	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	64.7630	68.5714%	30000000	600000000	9.2981	10.3837%	74.0611	71.8349%	3.2634%
PrimeNet	2⁶⁰	0.0416	63.3333%	16000	320000	0.0050	3.0821%	0.0466	64.4635%	1.1301%
GPU72	2⁶⁴	0.9647	65.6250%	22000	450000	0.0069	2.1046%	0.9716	66.3484%	0.7234%
Difference	+6	+63.7983	+2.9464%	+29978000	+599550000	+9.2912	+8.2791%	+73.0895	+5.4864%	+5.4864%

Known prime factors (1 factor, 89.3 bits, 0.00241991% 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
3689617	754332122146734320605876193	27	89.285	102223634884966965488 2⁴ × 6388977180310435343	2021-07-12	16	6388977180310435343	63,163,841	5.301e+10	9.901e+10

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-13T10:17:00	Carsten Kossendey	durandal	20000	260000		-		-	-	0.005	-	-	0.723%
2012-03-23T03:47:00	Squeeky_Squirrel	P4_2600	90000	1665000		-		-	-	0.027	-	-	1.887%
2016-07-09T02:37:06	Jocelyn Larouche	Manual testing	90000	3330000	6	-		-	-	0.041	-	-	2.223%
2016-12-26T21:22:48	Jocelyn Larouche	low 4M	108000	108000		-		-	-	0.016	-	-	0.696%
2016-12-29T20:13:43	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.776%
2017-01-19T17:19:08	Jocelyn Larouche	low 4M	155520	155520		-		-	-	0.024	-	-	0.862%
2017-02-04T18:42:36	Jocelyn Larouche	low 4M	186624	186624		-		-	-	0.028	-	-	0.954%
2017-02-08T21:16:25	Jocelyn Larouche	low 4M	223948	2239480	6	-		-	-	0.051	-	-	2.407%
2018-01-07T13:28:08	Jocelyn Larouche	low 4M	3689617	3689617		-		-	-	0.562	-	-	3.335%
2018-02-01T03:05:43	kkmrkkblmbrbk	c4.large	4000000	80000000	12	-		-	-	1.240	-	-	6.849%
2018-03-29T01:04:28	Jocelyn Larouche	low 4M	3689617	7379234	6	-		-	-	0.593	-	-	4.107%
2020-11-21T02:36:25	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.384%
2022-03-04T04:18:42	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.622%
2022-03-22T17:35:36	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.664%
2022-05-24T23:56:13	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.369%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-06T05:55:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-20T09:17:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.083	-	-
2012-06-05T02:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.433	-	-
2016-02-23T16:29:36	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.266	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.532	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.013	-	-
2015-10-20T08:54:42	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.025	-	-
2017-01-05T14:31:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.051	-	-
2018-07-30T10:36:13	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.101	-	-
2020-10-29T01:52:48	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.20	-	-
2020-10-29T01:52:48	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.41	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.482 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	2.482 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.628	53.355%
25	50000	0.058	94.351%
30	250000	0.004	99.633%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.788
50000	6800000	754332122146734320605876193	4	0.695

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-30T13:14:00	freeshow	dom	50000	5000000						3	0.447
2012-07-07T10:40:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.447
2015-10-29T19:30:29	driveByUpgrades	Build_4	50000	5000000						3	0.447
2017-05-31T13:32:50	Conductor	NataW	50000	5000000						3	0.447
2021-07-12T08:14:28	kutens	arcturus	50000	6800000	754332122146734320605876193	89.285	4	2	3542491313412595	4	0.695

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-10-11T00:00:00	ANONYMOUS	v4_computers	CC11624ACBF09717	0.388
1999-09-14T00:00:00	ANONYMOUS	v4_computers	CC11624ACBF09717	0.388

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-07-13T12:28:56

kutens

sol

754332122146734320605876193

808FE3B71D6237BF

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 = 4000000, B2 = 80000000 (P-1 stage 2)

B1 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3689617, B2 = 7379234 (P-1 stage 2)

B1 = 3689617 (P-1 stage 1)

B1 = 223948, B2 = 2239480 (P-1 stage 2)

B1 = 90000, B2 = 3330000 (P-1 stage 2)

B1 = 223948 (P-1 stage 1)

B1 = 186624 (P-1 stage 1)

B1 = 90000, B2 = 1665000 (P-1 stage 2)

B1 = 155520 (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 = 260000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

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TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

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2⁶³

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2⁶¹

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2¹⁰⁰

Last modified: 2022-05-24T23:56:13+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