M16808681 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	2⁷³	113.8010	65.7534%	1000000	503963130	22.5197	7.0922%	136.3207	68.1823%
Target	2⁶⁹	7.1027	63.7681%	120000	3200000	0.2282	3.2900%	7.3309	64.9601%
Difference	+4	+106.6983	+1.9853%	+880000	+500763130	+22.2915	+3.8022%	+128.9898	+3.2221%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16808681	429986304888223754891105663945002844137	39	128.338	12790602215849767001084310659028 2² × 3 × 547 × 1009 × 1733 × 5821 × 85133 × 99643 × 22567859	2022-05-12	99643	22567859	7.876e+9	1.0496	1.8208

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-10-19	ANONYMOUS	v4_computers	195000	2973750		-		-	-	0.275	-	-	2.242%
2022-05-12	alpertron	Manual testing	1000000	503963130			429986304888223754891105663945002844137	39	128.338	22.52	18.38	45.04	7.092%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-14	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2001-04-15	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.005	-	-
2001-07-17	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.434	-	-
2016-03-16	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.445	-	-
2014-09-15	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.889	-	-
2018-03-11	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	1.778	-	-
2018-03-11	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.557	-	-
2020-05-24	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	7.113	-	-
2021-09-01	lycorn	Manual testing	2⁷⁰	2⁷¹		-	-	14.23	-	-
2021-09-19	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	28.45	-	-
2021-11-26	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	56.91	-	-

ECM factoring results:

Total ECM effort:	0.831 GHz-days
Estimated T-Level:	0.192

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-12	ATH	ec2-1x	50000	5000000						1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-11-24	ANONYMOUS	v4_computers	DE037A782E1C9027	9.191
2006-04-14	ebravick	v4_computers	DE037A782E1C9027	9.191

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 = 1000000, B2 = 503963130 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 195000, B2 = 2973750 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁹

2⁵⁶

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