M3573761 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

860BBC401F637673

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	2⁷¹	133.7746	69.0141%	500000	130364850	1.1537	5.3628%	134.9282	70.6758%	1.6617%
PrimeNet	2⁶⁰	0.0430	63.3333%	15000	300000	0.0046	2.9713%	0.0476	64.4228%	1.0895%
GPU72	2⁶⁴	0.9960	65.6250%	20000	400000	0.0062	1.9778%	1.0022	66.3049%	0.6799%
Difference	+7	+132.7786	+3.3891%	+480000	+129964850	+1.1475	+3.3849%	+133.9261	+4.3709%	+4.3709%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

133.7746

69.0141%

500000

130364850

1.1537

5.3628%

134.9282

70.6758%

1.6617%

PrimeNet

2⁶⁰

0.0430

63.3333%

15000

300000

0.0046

2.9713%

0.0476

64.4228%

1.0895%

GPU72

2⁶⁴

0.9960

65.6250%

20000

400000

0.0062

1.9778%

1.0022

66.3049%

0.6799%

Difference

+132.7786

+3.3891%

+480000

+129964850

+1.1475

+3.3849%

+133.9261

+4.3709%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3573761	19894692275790794586157578481	29	94.006	2783439110196624030840 2³ × 3³ × 5 × 13 × 198250648874403421	2021-05-21	27	198250648874403421	1.720e+9	1.645e+9	3.072e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3573761

19894692275790794586157578481

94.006

2783439110196624030840
2³ × 3³ × 5 × 13 × 198250648874403421

2021-05-21

198250648874403421

1.720e+9

1.645e+9

3.072e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T04:57:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.604%
2011-12-23T12:48:00	Squeeky_Squirrel	P4_2600	85000	1572500		-		-	-	0.025	-	-	1.610%
2016-04-06T15:35:15	harlee	P4_2600	175000	4681250	6	-		-	-	0.064	-	-	2.446%
2017-05-13T15:56:56	Jocelyn Larouche	low 4M	350000	3500000	6	-		-	-	0.079	-	-	2.562%
2022-02-25T17:22:59	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.030	-	-	0.862%
2022-05-17T01:12:24	Jocelyn Larouche	Manual testing	500000	130364850		-		-	-	1.154	-	-	5.363%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:33	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.043	-	-
2009-03-15T08:10:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.043	-	-
2011-06-19T07:16:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.086	-	-
2012-07-02T04:03:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.447	-	-
2016-02-23T16:29:33	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.275	-	-
2015-01-30T19:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.549	-	-
2015-01-30T19:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.046	-	-
2016-02-26T10:03:26	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.091	-	-
2017-01-20T05:22:17	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.182	-	-
2018-11-19T15:52:44	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.364	-	-
2020-12-21T22:31:05	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.73	-	-
2021-03-18T11:36:12	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	33.46	-	-
2021-03-18T11:36:12	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	66.91	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.608 GHz-days
Estimated T-Level:	0.850

Digits	B1	Curves	Complete	FacMiss
20	11000	17 / 100	0.170	84.294%
25	50000	17 / 280	0.061	94.099%

New Calculation Method

Total ECM effort:	2.608 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.560	57.149%
25	50000	0.051	95.070%
30	250000	0.003	99.689%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.776
50000	6350000	19894692275790794586157578481	5	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-31T22:50:00	zampel	malissol	50000	5000000						3	0.444
2012-04-22T03:13:00	Piepen	T30-2200	50000	5000000						3	0.444
2015-07-03T04:53:00	joe b.	Pandora	50000	5000000						3	0.444
2017-03-25T04:23:04	Bruce	desk	50000	5000000						3	0.444
2021-05-21T16:06:35	nordi	sweet16	50000	6350000	19894692275790794586157578481	94.006	5	2	5209862349890397	5	0.831

date	userid	compid	res64	spent (GHz-days)
1999-10-07T00:00:00	ANONYMOUS	v4_computers	B1664161D0590B__	0.375

date

userid

compid

res64

spent (GHz-days)

1999-10-07T00:00:00

ANONYMOUS

v4_computers

B1664161D0590B__

0.375

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 = 500000, B2 = 130364850 (P-1 stage 2)

B1 = 350000, B2 = 3500000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 175000, B2 = 4681250 (P-1 stage 2)

B1 = 350000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 175000 (P-1 stage 1)

B1 = 85000, B2 = 1572500 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 20000, B2 = 245000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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