M8699063 Mersenne number exponent details

Residue

Status

L-L

5CBED1103F4CE7F2

double-checked

PRP

0C369AB6ABFEA42E

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	2⁷³	219.8908	67.1233%	100000	1875000	0.0745	1.5746%	219.9653	67.6410%	0.5177%
PrimeNet	2⁶⁴	0.4092	62.5000%	36000	1000000	0.0335	3.3089%	0.4427	63.7408%	1.2408%
GPU72	2⁶⁸	6.8519	64.7059%	55000	1200000	0.0444	2.2969%	6.8963	65.5166%	0.8107%
Difference	+5	+213.0390	+2.4174%	+45000	+675000	+0.0300	-0.7223%	+213.0690	+2.1244%	+2.1244%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

219.8908

67.1233%

100000

1875000

0.0745

1.5746%

219.9653

67.6410%

0.5177%

PrimeNet

2⁶⁴

0.4092

62.5000%

36000

1000000

0.0335

3.3089%

0.4427

63.7408%

1.2408%

GPU72

2⁶⁸

6.8519

64.7059%

55000

1200000

0.0444

2.2969%

6.8963

65.5166%

0.8107%

Difference

+213.0390

+2.4174%

+45000

+675000

+0.0300

-0.7223%

+213.0690

+2.1244%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8699063	28168481304739063796593	23	74.576	1619052609731592 2³ × 3 × 7 × 167 × 18133 × 3182479	2021-12-07	18133	3182479	743.68	0.0721	0.1226

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8699063

28168481304739063796593

74.576

1619052609731592
2³ × 3 × 7 × 167 × 18133 × 3182479

2021-12-07

18133

3182479

743.68

0.0721

0.1226

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-12-02T00:00:00	Team Prime Rib	v4_computers	50000	850000		-		-	-	0.035	-	-	1.060%
2012-01-17T14:11:00	bcp19	Manual testing	100000	1875000		-		-	-	0.074	-	-	1.575%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-12-07T16:40:22	masser	Manual testing	375000	9000000	2	7	28168481304739063796593	P-1	23	74.576	0.390

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-12-07T16:40:22

masser

Manual testing

375000

9000000

28168481304739063796593

P-1

74.576

0.390

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.035	-	-
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.071	-	-
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.183	-	-
2004-05-11T00:00:00	Sturle Sunde	v4_computers	2¹	2⁶⁴		-	-	0.409	-	-
2014-01-23T12:00:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.430	-	-
2015-05-26T22:23:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.859	-	-
2016-02-08T21:54:20	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.718	-	-
2018-04-24T19:00:11	monst	Manual testing	2⁶⁷	2⁶⁸		-	-	3.436	-	-
2020-02-28T11:42:08	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	6.872	-	-
2021-08-20T17:07:22	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	13.74	-	-
2021-08-28T13:06:22	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	27.49	-	-
2021-10-11T16:34:00	SRBase	Manual testing	2⁷¹	2⁷²		-	-	54.98	-	-
2021-12-11T16:31:44	masser	Manual testing	2⁷²	2⁷³		-	-	110.0	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.191 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	1.191 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	1.191

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-10-09T02:45:00	BloodIce	URM2	50000	5000000						3	1.191

date	userid	compid	res64	spent (GHz-days)
2000-08-31T00:00:00	ANONYMOUS	v4_computers	5CBED1103F4CE7F2	2.271
2002-12-09T00:00:00	Team Prime Rib	v4_computers	5CBED1103F4CE7F2	2.271

date

userid

compid

res64

spent (GHz-days)

2000-08-31T00:00:00

ANONYMOUS

v4_computers

5CBED1103F4CE7F2

2.271

2002-12-09T00:00:00

Team Prime Rib

v4_computers

5CBED1103F4CE7F2

2.271

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 = 9000000 (P-1 stage 2)

B1 = 375000 (P-1 stage 1)

B1 = 100000, B2 = 1875000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 50000, B2 = 850000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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