M2209717 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	26.9740	67.6471%	5000000	200000000	1.4896	8.9607%	28.4636	70.5461%	2.8990%
PrimeNet	2⁵⁸	0.0174	62.0690%	10000	180000	0.0018	2.8654%	0.0192	63.1558%	1.0869%
GPU72	2⁶²	0.2780	64.5161%	11000	170000	0.0019	1.6014%	0.2799	65.0844%	0.5683%
Difference	+6	+26.6960	+3.1309%	+4989000	+199830000	+1.4877	+7.3592%	+28.1837	+5.4617%	+5.4617%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2209717	4862111692275814064112601	25	82.008	1100166150750483900 2² × 3 × 5² × 1601 × 2290581200813	2020-04-16	1601	2290581200813	754,108	11,898	22,222

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.227%
2010-11-05T01:17:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.199%
2010-11-10T11:26:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.355%
2011-01-08T20:04:00	markr	tiny	90000	1665000		-		-	-	0.017	-	-	2.224%
2014-06-24T22:45:00	Jocelyn Larouche	Manual testing	119046	119046		-		-	-	0.011	-	-	0.890%
2014-10-17T00:38:00	Jocelyn Larouche	Manual testing	148092	148092		-		-	-	0.014	-	-	1.006%
2015-11-11T05:09:38	Alexander Dubrovin	Manual testing	1000000	2500000	6	-		-	-	0.103	-	-	3.303%
2015-12-08T16:57:52	Alexander Dubrovin	Manual testing	2000000	15000000	12	-		-	-	0.258	-	-	5.357%
2015-12-09T09:35:07	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.030%
2019-12-30T03:48:45	mikr	MSI	5000000	200000000	12	-		-	-	1.490	-	-	8.961%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-02T11:02:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T21:31:00	Sturle Sunde	dittersdorf.ifi	2⁶¹	2⁶²		-	-	0.139	-	-
2013-12-04T06:19:00	LaurV	Manual testing	2⁶²	2⁶³		-	-	0.444	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.888	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.691	-	-
2015-10-22T10:17:20	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.382	-	-
2016-12-12T15:11:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.764	-	-
2019-05-06T12:23:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.53	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.482 GHz-days
Estimated T-Level:	3.200

Digits	B1	Curves	Complete	FacMiss
20	11000	64 / 100	0.640	52.560%
25	50000	64 / 280	0.229	79.534%

New Calculation Method

Total ECM effort:	5.482 GHz-days
Estimated T-Level:	3.200

Digits	B1	Complete	FacMiss
20	11000	2.065	12.688%
25	50000	0.187	82.978%
30	250000	0.011	98.858%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		63	5.397
50000	5000000	4862111692275814064112601	1	0.086

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-08T05:08:00	paulie	iMac3.4	50000	5000000						3	0.257
2009-12-15T23:59:00	James Classen	towerofart	50000	5000000						3	0.257
2011-09-16T00:29:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.257
2013-06-02T05:06:00	jim f in mn	asus	50000	5000000						3	0.257
2015-03-14T09:13:00	Bruce	desk16	50000	5000000						3	0.257
2016-01-21T20:57:30	Jason U	Server7	50000	5000000						3	0.257
2016-03-14T00:13:01	Jason U	Server7	50000	5000000						3	0.257
2016-07-02T17:00:23	Bruce	Desk6	50000	5000000						3	0.257
2016-11-17T01:28:09	NBCC		50000	5000000						3	0.257
2017-05-02T10:11:49	Bruce	Desk6	50000	5000000						3	0.257
2017-11-15T10:49:21	J.R. Allen	lapacer	50000	5000000						3	0.257
2018-04-03T18:50:48	Bruce	Desk6	50000	5000000						3	0.257
2018-10-06T19:28:55	Bruce	Desk6	50000	5000000						3	0.257
2020-02-07T11:52:59	Keysarecool	Boat_Anchor	50000	5000000						3	0.257
2020-02-15T09:07:53	mnd9	libproj	50000	5000000						3	0.257
2020-02-22T21:10:20	mnd9	27016b	50000	5000000						3	0.257
2020-03-03T14:47:06	mat10243x	K3	50000	5000000						3	0.257
2020-03-06T20:47:08	kracker	O0	50000	5000000						3	0.257
2020-03-13T18:48:09	mnd9	office2	50000	5000000						3	0.257
2020-03-21T22:16:06	kracker	O0	50000	5000000						3	0.257
2020-04-04T03:39:50	Keysarecool	Boat_Anchor	50000	5000000						3	0.257
2020-04-16T18:40:17	Keysarecool	Boat_Anchor	50000	5000000	4862111692275814064112601	82.008	1	2	3487810583707340	1	0.086

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	F237CA866DA88329	0.145
2018-04-17T06:00:03	kkmrkkblmbrbk	old	F237CA866DA88329	0.145

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 2000000, B2 = 65000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2000000, B2 = 15000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1000000, B2 = 2500000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 90000, B2 = 1665000 (P-1 stage 2)

B1 = 148092 (P-1 stage 1)

B1 = 119046 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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