M3750631 Mersenne number exponent details

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M3750631

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is 2 ^3750631 - 1

has 1129053 decimal digits

takes 0.394 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	08E80066D576BC6E	double-checked
PRP	8B7FAF25D9E79F12	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	63.7094	68.5714%	1600000	66000000	0.7780	6.1487%	64.4875	70.5039%	1.9325%
PrimeNet	2⁶⁰	0.0410	63.3333%	16000	320000	0.0050	3.0909%	0.0459	64.4667%	1.1333%
GPU72	2⁶⁴	0.9490	65.6250%	22000	450000	0.0069	2.1107%	0.9559	66.3506%	0.7256%
Difference	+6	+62.7605	+2.9464%	+1578000	+65550000	+0.7711	+4.0380%	+63.5316	+4.1533%	+4.1533%

Known prime factors (1 factor, 70.6 bits, 0.00188270% 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
3750631	1805675568540014222599	22	70.613	240716237953029 3 × 47 × 1707207361369	2021-10-23	47	1707207361369	64.662	14,165	26,456

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T09:58:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	0.730%
2013-03-16T16:39:00	Squeeky_Squirrel	T7500_2200	110000	2035000		-		-	-	0.033	-	-	2.076%
2015-12-03T03:09:54	mikr	MSI	1600000	66000000	12	-		-	-	0.778	-	-	6.149%
2022-03-03T20:38:53	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.624%
2022-03-22T11:09:14	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.666%
2022-05-25T14:14:03	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.379%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-03T17:11:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-05-01T13:12:00	markr	Manual testing	2¹	2⁶²		-	-	0.164	-	-
2012-05-10T01:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.426	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.262	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.523	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.996	-	-
2016-02-26T17:45:26	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.992	-	-
2016-11-08T02:48:15	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.985	-	-
2019-02-11T13:34:42	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.970	-	-
2020-12-07T01:36:30	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	15.94	-	-
2021-03-22T17:40:37	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	31.88	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.705 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:	3.705 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.939	39.098%
25	50000	0.087	91.682%
30	250000	0.005	99.453%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	2.840
50000	6700000	1805675568540014222599	5	0.865

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-09T05:51:00	Marzbug	Xeon	50000	5000000						3	0.448
2012-06-02T13:56:00	Smurgs	Praca	50000	5000000						3	0.448
2015-12-07T17:58:44	driveByUpgrades	Build_4	50000	5000000						3	0.448
2017-07-12T17:55:02	bayanne	iMac	50000	5000000						3	0.448
2021-08-13T16:26:36	Gyuri	WIBE	50000	5000000						7	1.046
2021-10-23T11:51:45	kutens	spica	50000	6700000	1805675568540014222599	70.613	5	2	2826731084641734	5	0.865

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-08-16T00:00:00	ANONYMOUS	v4_computers	08E80066D576BC6E	0.394
1999-08-16T00:00:00	ANONYMOUS	v4_computers	08E80066D576BC6E	0.394

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-24T12:05:42

kutens

terra

1805675568540014222599

8B7FAF25D9E79F12

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

B1 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 110000, B2 = 2035000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-25T14:14:03+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