M6736799 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	Prob over default TF
Actual	2⁶⁹	17.7216	66.6667%	1000000	23000000	0.6952	5.7022%	18.4168	72.3689%	8.8768%
PrimeNet	2⁶³	0.2369	63.4921%	28000	700000	0.0204	3.1462%	0.2573	66.6383%	3.1462%
GPU72	2⁶⁷	4.4107	65.6716%	40000	900000	0.0275	2.1659%	4.4381	67.8375%	2.1659%
Difference	+2	+13.3109	+0.9950%	+960000	+22100000	+0.6677	+3.5364%	+13.9786	+4.5314%	+4.5314%

	GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
6736799	27356454920703278693461962691947013841	38	124.363	2030374879872716901117427037080 2³ × 5 × 23 × 67 × 71 × 221747 × 304781 × 681257 × 10076243	681257	10076243	2020-10-27	2.706e+10	0.3772	0.4384

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-06-23T18:48:00	Carsten Kossendey	leela	35000	533750		-		-	-	0.020	-	-	1.393%
2012-07-16T05:33:00	Nesowa	EPC	80000	1440000		-		-	-	0.049	-	-	2.208%
2019-03-25T00:32:57	takahashi	vaio	250000	4400000	6	-		-	-	0.151	-	-	3.484%
2020-10-27T00:04:11	takahashi	vaio	1000000	23000000	12		27356454920703278693461962691947013841	38	124.363	0.695	2.938	1.390	5.702%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05T00:00:00	ANONYMOUS	v4_computers	?	2⁶²		-	-	0.046	-	-
2004-07-26T00:00:00	ANONYMOUS	v4_computers	?	2⁶³		-	-	0.146	-	-
2014-06-29T00:28:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.291	-	-
2014-07-03T07:08:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.555	-	-
2015-11-12T20:33:11	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.109	-	-
2016-05-02T19:59:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.218	-	-
2018-02-27T02:58:05	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.437	-	-
2020-05-08T08:18:58	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.874	-	-

ECM factoring results:

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
2012-05-11T19:49:00	S00030	vd01	50000	5000000						3	0.995
2017-01-15T22:47:28	WileECoyote	penny	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	William B. Adams	v4_computers	7E288D1410E4DA__	1.469
1999-09-14T00:00:00	ANONYMOUS	v4_computers	C612EC98D992045A	1.469
2001-06-03T00:00:00	ANONYMOUS	v4_computers	5B60D808C4FC2C__	1.469
2001-11-03T00:00:00	Stephen	v4_computers	C612EC98D992045A	1.469

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-29T11:03:39

Lord Julius

Babybox

27356454920703278693461962691947013841

F14859DD24505921

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 = 23000000 (stage 2)

B1 = 1000000 (stage 1)

B1 = 250000, B2 = 4400000 (stage 2)

B1 = 250000 (stage 1)

B1 = 80000, B2 = 1440000 (stage 2)

B1 = 80000 (stage 1)

B1 = 35000, B2 = 533750 (stage 2)

B1 = 35000 (stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

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	<	123M	PrimeNet wavefront