M8626487 Mersenne number exponent details

Residue

Status

L-L

17B9905BA8B9E852

double-checked

PRP

64BCC6C75C7CA22A

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	110.8602	66.6667%	205000	4356250	0.1632	2.5150%	111.0234	67.5050%	0.8383%
PrimeNet	2⁶⁴	0.4126	62.5000%	36000	1000000	0.0335	3.3045%	0.4461	63.7392%	1.2392%
GPU72	2⁶⁸	6.9095	64.7059%	55000	1200000	0.0444	2.2938%	6.9540	65.5155%	0.8096%
Difference	+4	+103.9506	+1.9608%	+150000	+3156250	+0.1188	+0.2212%	+104.0694	+1.9896%	+1.9896%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

110.8602

66.6667%

205000

4356250

0.1632

2.5150%

111.0234

67.5050%

0.8383%

PrimeNet

2⁶⁴

0.4126

62.5000%

36000

1000000

0.0335

3.3045%

0.4461

63.7392%

1.2392%

GPU72

2⁶⁸

6.9095

64.7059%

55000

1200000

0.0444

2.2938%

6.9540

65.5155%

0.8096%

Difference

+103.9506

+1.9608%

+150000

+3156250

+0.1188

+0.2212%

+104.0694

+1.9896%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8626487	7042148749234958059577	22	72.577	408170136304324 2² × 29 × 3518708071589	2021-12-19	29	3518708071589	175.76	72,583	135,565

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8626487

7042148749234958059577

72.577

408170136304324
2² × 29 × 3518708071589

2021-12-19

3518708071589

175.76

72,583

135,565

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	ANONYMOUS	v4_computers	40000	40000		-		-	-	0.015	-	-	0.309%
2012-06-04T10:40:00	James Heinrich	3930K	205000	4356250		-		-	-	0.163	-	-	2.515%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-12-19T05:21:58	masser	Manual testing	375000	375000	2	7	7042148749234958059577	P+1	22	72.577	0.216

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.036	-	-
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.071	-	-
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.185	-	-
1999-10-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.413	-	-
2012-06-03T18:52:00	James Heinrich	Manual testing	2⁶⁴	2⁶⁵		-	-	0.433	-	-
2015-05-25T09:34:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.866	-	-
2016-02-03T20:13:19	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.733	-	-
2018-04-21T15:45:10	monst	Manual testing	2⁶⁷	2⁶⁸		-	-	3.465	-	-
2019-11-19T13:59:34	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	6.930	-	-
2021-08-22T16:36:53	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	13.86	-	-
2021-10-09T14:40:09	Sid & Andy	Manual testing	2⁷⁰	2⁷¹		-	-	27.72	-	-
2021-10-17T07:26:56	SRBase	Manual testing	2⁷¹	2⁷²		-	-	55.44	-	-

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
2013-08-22T13:19:00	fireredd	ont2	50000	5000000						3	1.191
2019-07-17T01:07:22	arnaud	CHAMOT06	50000	5000000						3	1.191

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-12-08T00:00:00	ANONYMOUS	v4_computers	17B9905BA8B9E852	2.252
2003-01-09T00:00:00	ANONYMOUS	v4_computers	17B9905BA8B9E852	2.252

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 = 205000, B2 = 4356250 (P-1 stage 2)

B1 = 375000 (P+1 stage 1)

B1 = 205000 (P-1 stage 1)

B1 = 40000 (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

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