M8616319 Mersenne number exponent details

Residue

Status

L-L

E5087575B9B5F0A9

double-checked

PRP

7FA62B3F4CDC4526

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	110.9910	66.6667%	100000	1850000	0.0740	1.7740%	111.0649	67.2580%	0.5913%
PrimeNet	2⁶⁴	0.4131	62.5000%	36000	1000000	0.0335	3.3038%	0.4466	63.7389%	1.2389%
GPU72	2⁶⁸	6.9177	64.7059%	55000	1200000	0.0444	2.2934%	6.9621	65.5153%	0.8094%
Difference	+4	+104.0733	+1.9608%	+45000	+650000	+0.0295	-0.5194%	+104.1028	+1.7427%	+1.7427%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

110.9910

66.6667%

100000

1850000

0.0740

1.7740%

111.0649

67.2580%

0.5913%

PrimeNet

2⁶⁴

0.4131

62.5000%

36000

1000000

0.0335

3.3038%

0.4466

63.7389%

1.2389%

GPU72

2⁶⁸

6.9177

64.7059%

55000

1200000

0.0444

2.2934%

6.9621

65.5153%

0.8094%

Difference

+104.0733

+1.9608%

+45000

+650000

+0.0295

-0.5194%

+104.1028

+1.7427%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8616319	2047095108247195918933201	25	80.760	118791743216981400 2³ × 3² × 5² × 3499 × 3877 × 4864901	2021-12-05	3877	4864901	32,848	0.1017	0.1874

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8616319

2047095108247195918933201

80.760

118791743216981400
2³ × 3² × 5² × 3499 × 3877 × 4864901

2021-12-05

3877

4864901

32,848

0.1017

0.1874

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-11-16T00:00:00	lozcs	v4_computers	40000	520000		-		-	-	0.025	-	-	0.987%
2012-01-13T06:08:00	bcp19	Manual testing	100000	1850000		-		-	-	0.074	-	-	1.774%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-12-05T15:09:25	masser	Manual testing	375000	8625000	2	7	2047095108247195918933201	P-1	25	80.760	0.383

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.071	-	-
1999-04-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.185	-	-
1999-10-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.413	-	-
2013-11-05T08:17:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.434	-	-
2015-05-25T09:34:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.867	-	-
2016-02-02T20:41:57	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.735	-	-
2018-04-21T08:30:12	monst	Manual testing	2⁶⁷	2⁶⁸		-	-	3.469	-	-
2019-11-20T05:04:55	masser	Manual testing	2⁶⁸	2⁶⁹		-	-	6.938	-	-
2021-08-21T15:36:24	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	13.88	-	-
2021-10-09T06:40:09	Sid & Andy	Manual testing	2⁷⁰	2⁷¹		-	-	27.75	-	-
2021-10-15T18:23:03	SRBase	Manual testing	2⁷¹	2⁷²		-	-	55.51	-	-

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
2013-08-20T15:27:00	BloodIce	URM2	50000	5000000						3	1.191
2019-08-26T20:47:41	arnaud	snd-15-157	50000	5000000						3	1.191

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-11-24T00:00:00	ANONYMOUS	v4_computers	E5087575B9B5F0A9	2.250
2002-11-24T00:00:00	lozcs	v4_computers	E5087575B9B5F0A9	2.250

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 = 1850000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 40000, B2 = 520000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

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