M3724937 Mersenne number exponent details

Residue

Status

L-L

F4B3E491E904A980

double-checked

PRP

9CDFDD22C7743E__

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	64.1489	68.5714%	1600000	66000000	0.7780	6.1442%	64.9269	70.5025%	1.9310%
PrimeNet	2⁶⁰	0.0412	63.3333%	16000	320000	0.0050	3.0872%	0.0462	64.4653%	1.1320%
GPU72	2⁶⁴	0.9555	65.6250%	22000	450000	0.0069	2.1081%	0.9624	66.3497%	0.7247%
Difference	+6	+63.1934	+2.9464%	+1578000	+65550000	+0.7711	+4.0360%	+63.9645	+4.1528%	+4.1528%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

64.1489

68.5714%

1600000

66000000

0.7780

6.1442%

64.9269

70.5025%

1.9310%

PrimeNet

2⁶⁰

0.0412

63.3333%

16000

320000

0.0050

3.0872%

0.0462

64.4653%

1.1320%

GPU72

2⁶⁴

0.9555

65.6250%

22000

450000

0.0069

2.1081%

0.9624

66.3497%

0.7247%

Difference

+63.1934

+2.9464%

+1578000

+65550000

+0.7711

+4.0360%

+63.9645

+4.1528%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3724937	44572182186720909051257	23	75.239	5982944434593244 2² × 31 × 201847 × 239040223	2021-10-09	201847	239040223	2,723.0	2.0124	3.7044

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3724937

44572182186720909051257

75.239

5982944434593244
2² × 31 × 201847 × 239040223

2021-10-09

201847

239040223

2,723.0

2.0124

3.7044

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T11:01:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	0.729%
2012-12-30T03:55:00	Squeeky_Squirrel	P4_2600	245000	7717500		-		-	-	0.099	-	-	3.249%
2021-01-04T01:22:37	Dylan Delgado	laptop-ryzen73700	1600000	66000000	12	-		-	-	0.778	-	-	6.144%
2022-03-03T23:55:48	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.623%
2022-03-22T11:10:16	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.665%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-06T05:54:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-29T04:00:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.082	-	-
2012-04-20T00:45:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.428	-	-
2016-02-23T16:29:37	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.264	-	-
2015-01-22T10:39:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.527	-	-
2015-01-22T10:39:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.003	-	-
2016-02-25T09:22:16	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.006	-	-
2016-11-02T03:53:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.012	-	-
2018-11-19T15:52:43	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.025	-	-
2020-12-12T10:56:22	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.05	-	-
2021-03-12T12:59:25	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.10	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.134 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	3.134 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.677	50.793%
25	50000	0.061	94.061%
30	250000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	2.836
50000	5000000	44572182186720909051257	2	0.299

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-07T07:26:00	Lupo	corpse	50000	5000000						3	0.448
2012-05-26T22:23:00	Piepen	T30-2200	50000	5000000						3	0.448
2015-11-22T19:35:08	S36049	Wolle5	50000	5000000						3	0.448
2017-06-21T17:16:52	Giuseppe Miano	favignana	50000	5000000						3	0.448
2021-08-03T16:11:32	PrimeNR		50000	5000000						7	1.045
2021-10-09T20:56:59	daveward2005	d12436	50000	5000000	44572182186720909051257	75.239	2	2	7081430485153190	2	0.299

date	userid	compid	res64	spent (GHz-days)
1998-08-09T00:00:00	ANONYMOUS	v4_computers	F4B3E491E904A980	0.391
1999-11-10T00:00:00	hetman	v4_computers	F4B3E491E904A980	0.391

date

userid

compid

res64

spent (GHz-days)

1998-08-09T00:00:00

ANONYMOUS

v4_computers

F4B3E491E904A980

0.391

1999-11-10T00:00:00

hetman

v4_computers

F4B3E491E904A980

0.391

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

B1 = 1600000 (P-1 stage 1)

B1 = 245000, B2 = 7717500 (P-1 stage 2)

B1 = 245000 (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)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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