M3758539 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

935A4E0C26B0CAED

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	63.5754	68.5714%	1600000	66000000	0.7780	6.1501%	64.3534	70.5043%	1.9329%
PrimeNet	2⁶⁰	0.0409	63.3333%	17000	340000	0.0053	3.1819%	0.0461	64.5000%	1.1667%
GPU72	2⁶⁴	0.9470	65.6250%	22000	450000	0.0069	2.1115%	0.9539	66.3508%	0.7258%
Difference	+6	+62.6284	+2.9464%	+1578000	+65550000	+0.7711	+4.0386%	+63.3995	+4.1535%	+4.1535%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

63.5754

68.5714%

1600000

66000000

0.7780

6.1501%

64.3534

70.5043%

1.9329%

PrimeNet

2⁶⁰

0.0409

63.3333%

17000

340000

0.0053

3.1819%

0.0461

64.5000%

1.1667%

GPU72

2⁶⁴

0.9470

65.6250%

22000

450000

0.0069

2.1115%

0.9539

66.3508%

0.7258%

Difference

+62.6284

+2.9464%

+1578000

+65550000

+0.7711

+4.0386%

+63.3995

+4.1535%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3758539	2503632534673860438001	22	71.085	333059273121000 2³ × 3 × 5³ × 111019757707	2021-08-17	125	111019757707	228.00	921.15	1,720.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3758539

2503632534673860438001

71.085

333059273121000
2³ × 3 × 5³ × 111019757707

2021-08-17

125

111019757707

228.00

921.15

1,720.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-11T19:28:00	Carsten Kossendey	durandal	20000	265000		-		-	-	0.005	-	-	0.730%
2013-03-19T02:07:00	Squeeky_Squirrel	P4_2600	110000	2035000		-		-	-	0.033	-	-	2.077%
2015-12-31T23:17:54	mikr	MSI	1600000	66000000	12	-		-	-	0.778	-	-	6.150%
2022-03-03T20:38:19	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.624%
2022-03-22T11:09:09	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.666%
2022-05-25T14:14:03	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.380%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-03T17:11:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-04-21T22:48:00	markr	Manual testing	2¹	2⁶²		-	-	0.163	-	-
2012-04-21T16:42:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.425	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.261	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.522	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.994	-	-
2016-02-28T22:17:31	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	1.988	-	-
2016-11-08T02:48:17	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	3.976	-	-
2019-01-28T14:25:38	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	7.953	-	-
2019-02-08T06:02:19	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	7.953	-	-
2020-11-16T18:25:20	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	15.91	-	-
2021-03-26T07:54:52	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	31.81	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.489 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	2.489 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.525	59.154%
25	50000	0.048	95.347%
30	250000	0.003	99.707%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.794
50000	6750000	2503632534673860438001	4	0.695

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-06T15:32:00	oodaira	Win02	50000	5000000						3	0.449
2012-06-06T18:35:00	sannerud.com	Jens2010	50000	5000000						3	0.449
2015-12-11T20:46:31	Bruce	agent86	50000	5000000						3	0.449
2017-07-19T15:02:53	driveByUpgrades	AMD8	50000	5000000						3	0.449
2021-08-17T21:13:47	nordi	sweet16	50000	6750000	2503632534673860438001	71.085	4	2	1483798554034457	4	0.695

date	userid	compid	res64	spent (GHz-days)
1999-09-22T00:00:00	ANONYMOUS	v4_computers	97258AA5734F17__	0.395

date

userid

compid

res64

spent (GHz-days)

1999-09-22T00:00:00

ANONYMOUS

v4_computers

97258AA5734F17__

0.395

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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