M6 954 613 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	2⁷²	137.5107	68.0556%	3500000	9616446840	166.7030	11.2991%	304.2137	71.6650%
Target	2⁶⁷	4.2725	65.6716%	45000	4500000	0.0910	2.2381%	4.3635	66.4400%
Difference	+5	+133.2381	+2.3839%	+3455000	+9611946840	+166.6120	+9.0610%	+299.8502	+5.2250%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6954613	32588744500515315677018077890209022326911	41	134.581	2342958874959348253958780876104035 3² × 5 × 13 × 929 × 10159 × 28517 × 149371 × 224513 × 443741971	2023-08-26	224513	443741971	2.137e+10	7.7112	14.277

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-06-20	Roman Maznichenko	WorkShop	85000	1615000		-		-	-	0.053	-	-	1.594%
2019-05-11	takahashi	vaio	300000	5000000	6	-		-	-	0.176	-	-	2.684%
2021-06-18	takahashi	vaio	1000000	30000000	12	-		-	-	0.816	-	-	4.562%
2023-08-26	Tha	Z-170	3500000	9616446840			32588744500515315677018077890209022326911	41	134.581	166.7	3.033	333.4	11.299%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-02	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2004-03-26	Sturle Sunde	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		-	-	1.075	-	-
2016-04-05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.149	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.298	-	-
2020-05-01	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.596	-	-
2021-08-01	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.19	-	-
2021-08-12	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.38	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.77	-	-

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
2012-09-02	Dogbert948	JONANDCALLIE	50000	5000000						3	0.995
2017-04-21	arnaud	snd-15-157	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Paul Victor Novarese	elroy0	3E6258DF3E3F80C7	1.516
1999-04-13	ANONYMOUS	v4_computers	3E6258DF3E3F80C7	1.516
2015-11-13	MadPoo	Manual testing	3E6258DF3E3F80C7	1.516

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 = 3500000, B2 = 9616446840 (P-1 stage 2)

B1 = 3500000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 300000, B2 = 5000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 85000, B2 = 1615000 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.9

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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