M6 957 043 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
Actual	2⁶⁸	8.5676	66.1765%	600000	12000000	0.3861	5.2841%	8.9536	67.9638%
Target	2⁶⁷	4.2711	65.6716%	45000	900000	0.0290	2.2383%	4.3000	66.4400%
Difference	+1	+4.2965	+0.5048%	+555000	+11100000	+0.3571	+3.0459%	+4.6536	+1.5238%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6957043	113119589737470336705192929	27	86.548	8129861331708768848 2⁴ × 7 × 17² × 521 × 249089 × 1935419	2020-01-23	249089	1935419	4,450,602	0.1078	0.1603

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-16	ANONYMOUS	v4_computers	35000	341250		-		-	-	0.016	-	-	1.412%
2011-12-11	James Heinrich	Q6600	130000	2827500		-		-	-	0.088	-	-	3.201%
2020-01-23	takahashi	vaio	600000	12000000	12		113119589737470336705192929	27	86.548	0.386	3.034	0.772	5.284%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-09	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2004-10-18	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.282	-	-
2014-02-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.537	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.074	-	-
2016-04-06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.148	-	-
2018-05-23	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.297	-	-

ECM factoring results:

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-09-08	vichico	HP-ROMA	50000	5000000						3	0.995
2017-04-24	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06	ANONYMOUS	v4_computers	44E43701E19AC69C	1.517
2001-10-25	ANONYMOUS	v4_computers	44E43701E19AC69C	1.517

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-01-26

Luigi Morelli

9800X

113119589737470336705192929

0CB9A5EFF9929D0B

2020-01-27

oodaira

com1

113119589737470336705192929

0CB9A5EFF9929D0B

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 = 600000, B2 = 12000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 130000, B2 = 2827500 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 35000, B2 = 341250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.8

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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