M3652387 Mersenne number exponent details

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M3652387

<<<

>>>

is 2 ^3652387 - 1

has 1099479 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	58B2E9AB0B30D9B7	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	65.4231	68.5714%	30000000	600000000	9.2981	10.3752%	74.7213	71.8322%	3.2608%
PrimeNet	2⁶⁰	0.0421	63.3333%	16000	320000	0.0050	3.0767%	0.0470	64.4615%	1.1281%
GPU72	2⁶⁴	0.9745	65.6250%	22000	400000	0.0065	2.0365%	0.9810	66.3250%	0.7000%
Difference	+6	+64.4486	+2.9464%	+29978000	+599600000	+9.2916	+8.3388%	+73.7402	+5.5072%	+5.5072%

Known prime factors (1 factor, 84.1 bits, 0.00230325% 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
3652387	21074677173227664353323343	26	84.124	2885055331380226733 97 × 1801109 × 16513624921	2021-09-02	1801109	16513624921	1,098,924	137.28	255.91

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T09:57:00	Carsten Kossendey	leela	20000	250000		-		-	-	0.005	-	-	0.713%
2012-01-30T02:45:00	Squeeky_Squirrel	P4_2600	90000	1642500		-		-	-	0.027	-	-	1.877%
2016-06-13T00:04:28	Jocelyn Larouche	Manual testing	108000	3285000	6	-		-	-	0.043	-	-	2.305%
2016-12-29T20:13:46	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.775%
2017-01-30T01:30:52	Jocelyn Larouche	low 4M	167520	167520		-		-	-	0.026	-	-	0.897%
2017-03-06T22:36:53	Squeeky_Squirrel	P4_2600	230000	6785000	12	-		-	-	0.089	-	-	3.121%
2017-03-07T20:00:41	Jocelyn Larouche	low 4M	241228	2412280	6	-		-	-	0.055	-	-	2.477%
2020-09-08T01:36:06	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.375%
2022-03-04T04:19:05	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.621%
2022-03-22T17:34:13	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.663%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:35	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-10T05:59:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-15T01:11:00	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	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.538	-	-
2015-01-22T10:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.023	-	-
2015-10-20T08:54:36	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.046	-	-
2016-12-28T15:57:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.092	-	-
2019-02-11T13:34:43	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.184	-	-
2020-11-08T06:31:47	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.37	-	-
2020-11-18T02:02:37	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.74	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.568 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	3.568 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.774	46.108%
25	50000	0.070	93.242%
30	250000	0.004	99.570%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.271
50000	5000000	21074677173227664353323343	2	0.297

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-17T11:13:00	LordJulius	Blackbox	50000	5000000						3	0.446
2012-06-14T22:49:00	Lukasz Wrobel	u-w	50000	5000000						3	0.446
2015-09-17T16:47:00	driveByUpgrades	Build_4	50000	5000000						3	0.446
2017-05-15T11:01:31	bayanne	iMac	50000	5000000						3	0.446
2020-11-24T14:33:24	axn	Manual testing	50000	5000000						10	1.487
2021-09-02T15:53:38	daveward2005	Dave2	50000	5000000	21074677173227664353323343	84.124	2	2	8451174373861492	2	0.297

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-16T00:00:00	ANONYMOUS	v4_computers	E9A93830C15CCC__	0.384

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-09-08T07:11:28

Oliver Kruse

IOS-2

21074677173227664353323343

58B2E9AB0B30D9B7

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 = 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)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-22T17:34:13+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