M3743897 Mersenne number exponent details

Residue

Status

L-L

95A164E5075CB124

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	63.8240	68.5714%	1600000	66000000	0.7780	6.1476%	64.6020	70.5035%	1.9321%
PrimeNet	2⁶⁰	0.0410	63.3333%	16000	320000	0.0050	3.0900%	0.0460	64.4663%	1.1330%
GPU72	2⁶⁴	0.9507	65.6250%	22000	450000	0.0069	2.1101%	0.9576	66.3503%	0.7253%
Difference	+6	+62.8733	+2.9464%	+1578000	+65550000	+0.7711	+4.0375%	+63.6444	+4.1532%	+4.1532%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

63.8240

68.5714%

1600000

66000000

0.7780

6.1476%

64.6020

70.5035%

1.9321%

PrimeNet

2⁶⁰

0.0410

63.3333%

16000

320000

0.0050

3.0900%

0.0460

64.4663%

1.1330%

GPU72

2⁶⁴

0.9507

65.6250%

22000

450000

0.0069

2.1101%

0.9576

66.3503%

0.7253%

Difference

+62.8733

+2.9464%

+1578000

+65550000

+0.7711

+4.0375%

+63.6444

+4.1532%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3743897	1240215418039861671088057544085552491119	40	129.866	165631615672100710982174128199247 3 × 44170017893 × 1249955086980315424993	2022-01-27	44170017893	1249955086980315424993	4.174e+10	1.037e+13	1.937e+13

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3743897

1240215418039861671088057544085552491119

129.866

165631615672100710982174128199247
3 × 44170017893 × 1249955086980315424993

2022-01-27

44170017893

1249955086980315424993

4.174e+10

1.037e+13

1.937e+13

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:43:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	0.730%
2013-03-05T23:56:00	Squeeky_Squirrel	E8400_3000	110000	2035000		-		-	-	0.033	-	-	2.075%
2015-11-08T10:04:23	mikr	MSI	1600000	66000000	12	-		-	-	0.778	-	-	6.148%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-05T06:52:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-05-08T12:21:00	markr	Manual testing	2¹	2⁶²		-	-	0.164	-	-
2012-05-10T01:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.426	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.262	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.524	-	-
2015-01-23T13:17:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.998	-	-
2016-02-26T10:03:30	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.996	-	-
2016-11-05T16:44:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.992	-	-
2018-07-23T16:23:30	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.984	-	-
2020-12-09T01:38:34	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	15.97	-	-
2021-03-20T01:45:12	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	31.94	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.034 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	4.034 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		26	3.885
50000	5000000	1240215418039861671088057544085552491119	1	0.149

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-05T01:36:00	willreid	jing	50000	5000000						3	0.448
2012-05-28T15:02:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.448
2015-12-05T15:20:03	Richard Kint	Desktop	50000	5000000						3	0.448
2017-07-18T03:51:30	jafarism	jafarism-r07	50000	5000000						3	0.448
2021-08-13T08:27:54	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						7	1.046
2021-10-20T04:31:19	RIHATEC	i7-3770K	50000	5000000						7	1.046
2022-01-27T09:19:34	daveward2005	Dave2	50000	5000000	1240215418039861671088057544085552491119	129.866	1	2	8222742955023269	1	0.149

date	userid	compid	res64	spent (GHz-days)
1998-02-24T00:00:00	ANONYMOUS	v4_computers	95A164E5075CB124	0.393
1999-11-04T00:00:00	MadPoo	v4_computers	95A164E5075CB124	0.393

date

userid

compid

res64

spent (GHz-days)

1998-02-24T00:00:00

ANONYMOUS

v4_computers

95A164E5075CB124

0.393

1999-11-04T00:00:00

MadPoo

v4_computers

95A164E5075CB124

0.393

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-02-03T06:54:15

_p95holder_

TFL16_PRPt11-E_b

1240215418039861671088057544085552491119

63730079B4AE47EE

2022-02-03T21:46:45

Oliver Kruse

11700K

1240215418039861671088057544085552491119

63730079B4AE47EE

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

B1 = 110000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10³

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10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

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