M6 998 561 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	8.5167	66.1765%	435000	11418750	0.3267	5.0564%	8.8435	67.8867%
Target	2⁶⁷	4.2457	65.6716%	45000	7200000	0.1375	2.2405%	4.3832	66.4408%
Difference	+1	+4.2710	+0.5048%	+390000	+4218750	+0.1893	+2.8159%	+4.4603	+1.4460%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6998561	351356342284695128897	21	68.251	25102041854368 2⁵ × 784438807949	2020-04-03	32	784438807949	14.670	13,513	25,239

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-01-21	ANONYMOUS	v4_computers	75000	937500		-		-	-	0.039	-	-	2.222%
2001-04-01	quantumfoam5678	v4_computers	75000	937500		-		-	-	0.039	-	-	2.222%
2001-10-20	ANONYMOUS	v4_computers	35000	481250		-		-	-	0.019	-	-	1.564%
2014-08-17	Nesowa	newfs	435000	11418750		-		-	-	0.327	-	-	5.056%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-29	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2001-01-21	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-14	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.534	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.068	-	-
2016-04-28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.136	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.271	-	-
2020-04-03	TJAOI	Manual testing	2⁶⁸	2⁶⁹*	351356342284695128897	68.251	21	6.153	3.081	12.42

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
2012-09-22	driveByUpgrades	Build_1	50000	5000000						3	0.995
2017-05-21	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	George Woltman		F8B9019B314BFB46	1.526
2001-11-03	ANONYMOUS	v4_computers	F8B9019B314BFB46	1.526

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-04-05

Oliver Kruse

Threadripper-PC

351356342284695128897

285A77896C9AEF9C

2020-04-07

marssystems

SYSTEM01

351356342284695128897

285A77896C9AEF9C

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 = 435000, B2 = 11418750 (P-1 stage 2)

B1 = 435000 (P-1 stage 1)

B1 = 75000, B2 = 937500 (P-1 stage 2)

B1 = 75000 (P-1 stage 1)

B1 = 35000, B2 = 481250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

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

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