M8605237 Mersenne number exponent details

Residue

Status

L-L

37C7BD9A2B323330

double-checked

PRP

432C211374E2C4CC

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	2⁷²	111.1339	66.6667%	100000	1825000	0.0734	1.7675%	111.2074	67.2558%	0.5892%
PrimeNet	2⁶⁴	0.4136	62.5000%	36000	1000000	0.0335	3.3032%	0.4471	63.7387%	1.2387%
GPU72	2⁶⁸	6.9266	64.7059%	55000	1200000	0.0444	2.2929%	6.9710	65.5151%	0.8093%
Difference	+4	+104.2073	+1.9608%	+45000	+625000	+0.0290	-0.5254%	+104.2363	+1.7407%	+1.7407%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

111.1339

66.6667%

100000

1825000

0.0734

1.7675%

111.2074

67.2558%

0.5892%

PrimeNet

2⁶⁴

0.4136

62.5000%

36000

1000000

0.0335

3.3032%

0.4471

63.7387%

1.2387%

GPU72

2⁶⁸

6.9266

64.7059%

55000

1200000

0.0444

2.2929%

6.9710

65.5151%

0.8093%

Difference

+104.2073

+1.9608%

+45000

+625000

+0.0290

-0.5254%

+104.2363

+1.7407%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8605237	23677968790994091143016583482737	32	104.223	1375788301414248738472664 2³ × 13 × 73 × 1976243 × 91696987511669	2021-11-25	1976243	91696987511669	1.625e+10	1,891,506	3,532,805

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8605237

23677968790994091143016583482737

104.223

1375788301414248738472664
2³ × 13 × 73 × 1976243 × 91696987511669

2021-11-25

1976243

91696987511669

1.625e+10

1,891,506

3,532,805

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-11-09T00:00:00	Matthew	v4_computers	40000	420000		-		-	-	0.023	-	-	0.925%
2012-02-10T22:39:00	bcp19	Turion_x2	100000	1825000		-		-	-	0.073	-	-	1.768%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-11-25T01:23:43	masser	Manual testing	375000	8625000	2	7	23677968790994091143016583482737	P+1	32	104.223	0.383

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.071	-	-
1998-12-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.185	-	-
2002-11-09T00:00:00	Matthew	v4_computers	2¹	2⁶⁴		-	-	0.414	-	-
2013-11-04T06:39:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.434	-	-
2015-05-25T09:34:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.868	-	-
2016-02-01T20:29:30	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.737	-	-
2018-04-25T11:45:10	monst	Manual testing	2⁶⁷	2⁶⁸		-	-	3.474	-	-
2019-11-09T19:20:04	masser	Manual testing	2⁶⁸	2⁶⁹		-	-	6.947	-	-
2021-08-22T16:41:41	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	13.89	-	-
2021-10-09T02:40:08	Sid & Andy	Manual testing	2⁷⁰	2⁷¹		-	-	27.79	-	-
2021-10-15T18:24:44	SRBase	Manual testing	2⁷¹	2⁷²		-	-	55.58	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.382 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	2.382 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	2.382

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-08-14T07:47:00	AdolfNor	Stargate	50000	5000000						3	1.191
2019-06-07T05:52:30	arnaud	snd-15-157	50000	5000000						3	1.191

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-12-30T00:00:00	ANONYMOUS	v4_computers	37C7BD9A2B323330	2.247
2003-05-11T00:00:00	Scali	v4_computers	37C7BD9A2B323330	2.247

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 = 375000, B2 = 8625000 (P+1 stage 2)

B1 = 375000 (P+1 stage 1)

B1 = 100000, B2 = 1825000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 40000, B2 = 420000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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