M7090613 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	4.1906	65.6716%	85000	1551250	0.0521	2.9145%	4.2427	66.6721%	3.1801%
PrimeNet	2⁶³	0.2251	63.4921%	30000	800000	0.0227	3.3204%	0.2478	64.7043%	1.2122%
GPU72	2⁶⁷	4.1906	65.6716%	45000	1000000	0.0307	2.3047%	4.2213	66.4628%	0.7912%
Difference	-	-	-	+40000	+551250	+0.0215	+0.6098%	+0.0215	+0.2093%	+0.2093%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7090613	73788858748680091871	20	66.00004	5203277822995 5 × 7 × 23 × 41 × 157651199	2016-08-25	41	157651199	2.1627	2.7158	5.0723

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-03T00:00:00	ANONYMOUS	v4_computers	35000	498750		-		-	-	0.019	-	-	1.813%
2011-12-23T14:25:00	bcp19	Manual testing	85000	1551250		-		-	-	0.052	-	-	2.914%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-07T00:00:00	ANONYMOUS	v4_computers	?	2⁶²		-	-	0.043	-	-
2001-11-03T00:00:00	ANONYMOUS	v4_computers	?	2⁶³		-	-	0.138	-	-
2014-02-06T08:13:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.277	-	-
2014-02-09T01:29:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.527	-	-
2015-06-16T01:49:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.054	-	-
2016-08-24T16:34:02	kkmrkkblmbrbk	Manual testing	2⁶⁶	2⁶⁷	73788858748680091871	66.00004	20	0.080	3.141	0.162

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.995 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:	0.995 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	0.995

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-10-14T07:25:00	Donna Noble	3570K-black	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-26T00:00:00	Stephen Wood	v4_computers	385843BCF8153DDA	1.546
1999-10-07T00:00:00	ANONYMOUS	v4_computers	8F35C5DA485A2B__	1.546
2001-11-10T00:00:00	ANONYMOUS	v4_computers	385843BCF8153DDA	1.546

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-02-09T17:59:42

Oliver Kruse

GTX-6

73788858748680091871

7DC1DAB82BD2BB__

2019-03-13T11:45:18

ATH

ec2-PRPCFDC

73788858748680091871

7DC1DAB82BD2BB64

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 = 85000, B2 = 1551250 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 498750 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

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10³

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10⁸

10⁹

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