M3602803 Mersenne number exponent details

Residue

Status

L-L

90C22BF8A9FA15C0

double-checked

PRP

6D11BEB5DA6E08__

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	2⁶⁹	33.1372	68.1159%	15000000	1000000000	10.4571	11.4906%	43.5943	71.7796%	3.6637%
PrimeNet	2⁶⁰	0.0426	63.3333%	15000	300000	0.0046	2.9755%	0.0473	64.4244%	1.0910%
GPU72	2⁶⁴	0.9879	65.6250%	20000	400000	0.0062	1.9807%	0.9941	66.3059%	0.6809%
Difference	+5	+32.1493	+2.4909%	+14980000	+999600000	+10.4509	+9.5099%	+42.6002	+5.4737%	+5.4737%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

33.1372

68.1159%

15000000

1000000000

10.4571

11.4906%

43.5943

71.7796%

3.6637%

PrimeNet

2⁶⁰

0.0426

63.3333%

15000

300000

0.0046

2.9755%

0.0473

64.4244%

1.0910%

GPU72

2⁶⁴

0.9879

65.6250%

20000

400000

0.0062

1.9807%

0.9941

66.3059%

0.6809%

Difference

+32.1493

+2.4909%

+14980000

+999600000

+10.4509

+9.5099%

+42.6002

+5.4737%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3602803	1577571172192804643311	22	70.418	218936640747885 3 × 5 × 241 × 60563386099	2020-10-27	241	60563386099	116.97	502.51	938.54

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3602803

1577571172192804643311

70.418

218936640747885
3 × 5 × 241 × 60563386099

2020-10-27

241

60563386099

116.97

502.51

938.54

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:45:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.823%
2011-11-22T17:16:00	markr	tiny	240000	6120000		-		-	-	0.085	-	-	3.417%
2020-05-23T14:46:28	axn	Manual testing	15000000	600000000	12	-		-	-	7.138	-	-	10.771%
2020-07-28T13:37:32	axn	Manual testing	15000000	1000000000	12	-		-	-	10.46	-	-	11.491%
2022-03-04T19:29:56	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.716%
2022-03-22T11:09:30	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.763%
2022-05-25T14:14:16	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.848%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	RPardoe	v4_computers	2¹	2⁶⁰		-	-	0.043	-	-
2009-03-12T16:38:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.043	-	-
2011-06-12T11:20:00	markr	Manual testing	2¹	2⁶²		-	-	0.171	-	-
2012-06-05T02:28:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.443	-	-
2016-02-23T16:29:34	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.272	-	-
2015-01-20T20:49:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.545	-	-
2015-01-20T20:49:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.037	-	-
2015-10-19T08:19:15	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.074	-	-
2016-12-21T02:23:31	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.148	-	-
2019-02-11T13:34:44	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.297	-	-
2020-10-18T02:09:38	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.59	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.224 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	2.224 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.577	56.162%
25	50000	0.053	94.802%
30	250000	0.003	99.664%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	1.927
50000	5000000	1577571172192804643311	2	0.297

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-14T16:34:00	borkencode	CFF2DC1CD	50000	5000000						3	0.445
2012-04-29T00:37:00	S36049	Wolle5	50000	5000000						3	0.445
2015-08-06T01:10:00	driveByUpgrades	Build_4	50000	5000000						3	0.445
2017-04-11T17:49:33	Bruce	Desk10	50000	5000000						3	0.445
2020-10-27T14:30:41	axn	Manual testing	50000	5000000	1577571172192804643311	70.418	2	2	4817305867964990	2	0.297
2020-10-27T14:30:41	axn	Manual testing	50000	5000000						1	0.148

date	userid	compid	res64	spent (GHz-days)
1998-02-08T00:00:00	RPardoe	v4_computers	90C22BF8A9FA15C0	0.378
1999-07-27T00:00:00	ANONYMOUS	v4_computers	90C22BF8A9FA15C0	0.378

date

userid

compid

res64

spent (GHz-days)

1998-02-08T00:00:00

RPardoe

v4_computers

90C22BF8A9FA15C0

0.378

1999-07-27T00:00:00

ANONYMOUS

v4_computers

90C22BF8A9FA15C0

0.378

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 = 15000000, B2 = 1000000000 (P-1 stage 2)

B1 = 15000000, B2 = 600000000 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 240000, B2 = 6120000 (P-1 stage 2)

B1 = 240000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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