M6 934 621 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	137.9071	68.0556%	2000000	258849360	5.0569	6.9793%	142.9641	70.2851%
Target	2⁶⁷	4.2849	65.6716%	45000	7200000	0.1375	2.2371%	4.4223	66.4396%
Difference	+5	+133.6223	+2.3839%	+1955000	+251649360	+4.9195	+4.7423%	+138.5417	+3.8455%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6934621	49939648840328093229151	23	75.403	3600748248558075 3² × 5² × 31 × 26497 × 19482821	2021-12-06	26497	19482821	1,250.3	0.3435	0.6268

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-31	ANONYMOUS	v4_computers	35000	516250		-		-	-	0.019	-	-	0.908%
2002-02-03	ANONYMOUS	v4_computers	35000	341250		-		-	-	0.016	-	-	0.799%
2012-08-17	Nesowa	EPC	85000	1508750		-		-	-	0.051	-	-	1.565%
2019-04-30	takahashi	vaio	300000	5000000	6	-		-	-	0.176	-	-	2.683%
2021-06-02	Dylan Delgado	Manual testing	630000	18900000	12	-		-	-	0.514	-	-	3.948%
2021-12-06	Seth_Tr	Manual testing	2000000	258849360			49939648840328093229151	23	75.403	5.057	3.024	10.11	6.979%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-03-06	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.230	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.283	-	-
2014-02-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.539	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.078	-	-
2016-04-03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.155	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.310	-	-
2020-05-01	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.621	-	-
2021-07-24	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.24	-	-
2021-08-11	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.48	-	-
2021-09-26	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.97	-	-

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
2012-08-21	Clown_Royal	lab2	50000	5000000						3	0.995
2017-05-03	Benoit Germain	ANN-BGERMAIN	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15	ANONYMOUS	v4_computers	194C3898A40032__	1.512
1999-06-26	netconx	v4_computers	8BB9122F394FFBF1	1.512
2002-03-31	ANONYMOUS	v4_computers	8BB9122F394FFBF1	1.512

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 = 2000000, B2 = 258849360 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 630000, B2 = 18900000 (P-1 stage 2)

B1 = 630000 (P-1 stage 1)

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

B1 = 300000 (P-1 stage 1)

B1 = 85000, B2 = 1508750 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 516250 (P-1 stage 2)

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

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.8

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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