M3690941 Mersenne number exponent details

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M3690941

<<<

>>>

is 2 ^3690941 - 1

has 1111084 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	C1E509A1336C0C7C	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁰	64.7398	68.5714%	30000000	600000000	9.2981	10.3840%	74.0379	71.8350%	3.2635%
PrimeNet	2⁶⁰	0.0416	63.3333%	16000	320000	0.0050	3.0823%	0.0466	64.4635%	1.1302%
GPU72	2⁶⁴	0.9643	65.6250%	22000	450000	0.0069	2.1047%	0.9712	66.3485%	0.7235%
Difference	+6	+63.7754	+2.9464%	+29978000	+599550000	+9.2912	+8.2793%	+73.0666	+5.4865%	+5.4865%

Known prime factors (1 factor, 75.1 bits, 0.00203537% 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
3690941	41175920500854661295759	23	75.124	5577970563720019 31 × 109 × 1033 × 1598040217	2021-09-04	1033	1598040217	2,350.9	13.259	24.765

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-13T20:54:00	Carsten Kossendey	durandal	20000	260000		-		-	-	0.005	-	-	0.723%
2012-03-23T22:31:00	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%
2016-12-26T21:22:49	Jocelyn Larouche	low 4M	108000	108000		-		-	-	0.016	-	-	0.696%
2016-12-29T20:13:44	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.776%
2017-01-19T17:19:09	Jocelyn Larouche	low 4M	155520	155520		-		-	-	0.024	-	-	0.862%
2017-02-04T18:42:37	Jocelyn Larouche	low 4M	186624	186624		-		-	-	0.028	-	-	0.954%
2017-02-13T00:36:32	Jocelyn Larouche	low 4M	223948	2239480	6	-		-	-	0.051	-	-	2.407%
2017-03-01T13:23:06	Squeeky_Squirrel	P4_2600	235000	6932500	12	-		-	-	0.091	-	-	3.151%
2020-11-24T01:44:27	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.384%
2022-03-04T04:18:41	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.622%
2022-03-22T11:10:13	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.664%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:36	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-07T17:51:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-22T01:38:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.083	-	-
2012-06-05T02:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.432	-	-
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		-	-	1.012	-	-
2015-10-20T08:54:43	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.025	-	-
2017-01-05T14:31:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.049	-	-
2018-07-23T16:23:33	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.098	-	-
2020-10-30T02:11:43	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.20	-	-
2020-10-30T02:11:43	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.39	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.873 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	3.873 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	0.839	43.227%
25	50000	0.076	92.700%
30	250000	0.005	99.534%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	2.831
50000	5000000	41175920500854661295759	7	1.043

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-24T21:41:00	S00030	vd01	50000	5000000						3	0.447
2012-07-07T19:51:00	oodaira	Linux01	50000	5000000						3	0.447
2015-10-31T07:47:33	FreeTibet	DR	50000	5000000						3	0.447
2017-06-01T21:48:44	he4var		50000	5000000						3	0.447
2021-07-15T05:53:03	tottenhoff	Garage-Band-003	50000	5000000						7	1.043
2021-09-04T14:07:45	daveward2005	d12436	50000	5000000	41175920500854661295759	75.124	7	2	289637792053984	7	1.043

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-11-24T00:00:00	ANONYMOUS	v4_computers	C1E509A1336C0C7C	0.388

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-09-11T13:35:03

kracker

GRID-11

41175920500854661295759

0DA22FC0BA72C1__

2021-09-12T03:53:09

Oliver Kruse

IOS-2

41175920500854661295759

0DA22FC0BA72C131

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 = 235000, B2 = 6932500 (P-1 stage 2)

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

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

B1 = 235000 (P-1 stage 1)

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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-22T11:10:13+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