M6 978 281 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	137.0443	68.0556%	3500000	9616446840	166.7030	11.3023%	303.7473	71.6660%
Target	2⁶⁷	4.2581	65.6716%	45000	7200000	0.1375	2.2394%	4.3955	66.4404%
Difference	+5	+132.7862	+2.3839%	+3455000	+9609246840	+166.5655	+9.0630%	+299.3518	+5.2256%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6978281	493563589728894035920224710318733979817	39	128.537	35364267340975093717222386882868 2² × 43 × 2029 × 2399 × 4931 × 15797 × 67931 × 7982635417	2023-09-11	67931	7982635417	2.001e+10	137.53	256.83

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	30000	30000		-		-	-	0.009	-	-	0.235%
2011-09-07	Carsten Kossendey	mother	440000	13530000		-		-	-	0.365	-	-	3.520%
2021-11-19	Seth_Tr	Manual testing	3000000	75000000	12	-		-	-	2.189	-	-	5.987%
2023-09-11	Tha	Z-170	3500000	9616446840			493563589728894035920224710318733979817	39	128.537	166.7	3.043	333.4	11.302%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2005-08-16	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-15	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.535	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.071	-	-
2016-04-26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.142	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.283	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.567	-	-
2021-08-09	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.13	-	-
2021-09-06	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.27	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.53	-	-

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
2012-09-11	MadPoo	IntLAVH03	50000	5000000						3	0.995
2017-05-17	Terçariol, C. A. S.	Manual testing	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	ANONYMOUS	v4_computers	A7A58F2542C937A1	1.522
2001-11-03	ANONYMOUS	v4_computers	A7A58F2542C937A1	1.522

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 = 3000000, B2 = 75000000 (P-1 stage 2)

B1 = 3500000 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 440000, B2 = 13530000 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 30000 (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

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