M3612607 Mersenne number exponent details

Residue

Status

L-L

E7BF11F49C3089B3

double-checked

PRP

4800C10DFB908E7F

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	33.0473	68.1159%	15000000	1000000000	10.4571	11.4931%	43.5044	71.7804%	3.6645%
PrimeNet	2⁶⁰	0.0425	63.3333%	15000	300000	0.0046	2.9770%	0.0472	64.4249%	1.0915%
GPU72	2⁶⁴	0.9853	65.6250%	20000	400000	0.0062	1.9817%	0.9915	66.3062%	0.6812%
Difference	+5	+32.0620	+2.4909%	+14980000	+999600000	+10.4509	+9.5114%	+42.5129	+5.4742%	+5.4742%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

33.0473

68.1159%

15000000

1000000000

10.4571

11.4931%

43.5044

71.7804%

3.6645%

PrimeNet

2⁶⁰

0.0425

63.3333%

15000

300000

0.0046

2.9770%

0.0472

64.4249%

1.0915%

GPU72

2⁶⁴

0.9853

65.6250%

20000

400000

0.0062

1.9817%

0.9915

66.3062%

0.6812%

Difference

+32.0620

+2.4909%

+14980000

+999600000

+10.4509

+9.5114%

+42.5129

+5.4742%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3612607	247483627879981792928497753	27	87.677	34252774780093958868 2² × 3 × 13 × 23 × 23203 × 411433058887	2021-06-23	23203	411433058887	13,611,164	3,413.7	6,375.9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3612607

247483627879981792928497753

87.677

34252774780093958868
2² × 3 × 13 × 23 × 23203 × 411433058887

2021-06-23

23203

411433058887

13,611,164

3,413.7

6,375.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:47:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.824%
2011-12-02T18:47:00	markr	tiny	240000	6180000		-		-	-	0.086	-	-	3.426%
2020-06-05T15:12:57	axn	Manual testing	15000000	450000000	12	-		-	-	5.894	-	-	10.365%
2020-08-03T12:55:16	axn	Manual testing	15000000	1000000000	12	-		-	-	10.46	-	-	11.493%
2022-03-04T04:19:38	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.716%
2022-03-22T17:35:38	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.764%
2022-05-24T23:56:14	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.850%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.043	-	-
2009-03-12T16:38:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.043	-	-
2011-06-02T03:05:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.085	-	-
2012-06-20T01:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.442	-	-
2016-02-23T16:29:34	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.272	-	-
2015-01-20T20:49:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.543	-	-
2015-01-20T20:49:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.034	-	-
2015-10-18T15:17:01	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.069	-	-
2016-12-23T23:58:56	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.137	-	-
2018-12-17T13:21:49	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.274	-	-
2020-10-19T15:15:44	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.55	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.557 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:	2.557 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.657	51.844%
25	50000	0.061	94.086%
30	250000	0.004	99.616%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.225
50000	6300000	247483627879981792928497753	2	0.332

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-15T02:06:00	Sid & Andy	Slinky	50000	5000000						3	0.445
2012-05-13T19:02:00	driveByUpgrades	_Compac_desk	50000	5000000						3	0.445
2015-08-13T16:09:00	driveByUpgrades	Build_4	50000	5000000						3	0.445
2017-04-21T16:32:27	bayanne	iMac	50000	5000000						3	0.445
2020-11-06T01:34:10	axn	Manual testing	50000	5000000						3	0.445
2021-06-23T22:09:20	kutens	capella	50000	6300000	247483627879981792928497753	87.677	2	2	5125038545091088	2	0.332

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	ANONYMOUS	v4_computers	E7BF11F49C3089B3	0.379
1999-07-30T00:00:00	ANONYMOUS	v4_computers	E7BF11F49C3089B3	0.379

date

userid

compid

res64

spent (GHz-days)

1998-05-08T00:00:00

ANONYMOUS

v4_computers

E7BF11F49C3089B3

0.379

1999-07-30T00:00:00

ANONYMOUS

v4_computers

E7BF11F49C3089B3

0.379

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 = 450000000 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

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

B1 = 240000, B2 = 6180000 (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)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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