M2219801 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	26.8515	67.6471%	2000000	65000000	0.5179	7.0333%	27.3694	69.9225%	2.2755%
PrimeNet	2⁵⁸	0.0173	62.0690%	10000	180000	0.0018	2.8678%	0.0191	63.1568%	1.0878%
GPU72	2⁶²	0.2768	64.5161%	11000	180000	0.0019	1.6299%	0.2787	65.0945%	0.5783%
Difference	+6	+26.5747	+3.1309%	+1989000	+64820000	+0.5160	+5.4035%	+27.0907	+4.8281%	+4.8281%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2219801	109660552183222375915807	24	76.537	24700536710998503 3 × 431 × 19103276651971	2020-04-08	431	19103276651971	7,883.7	99,227	185,329

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.227%
2010-10-12T03:39:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.674%
2010-12-20T10:21:00	Oscar Östlin		85000	1593750		-		-	-	0.016	-	-	2.175%
2014-05-26T23:57:00	Jocelyn Larouche	Manual testing	113914	113914		-		-	-	0.011	-	-	0.868%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	142828	142828		-		-	-	0.014	-	-	0.987%
2015-04-30T06:37:00	Squeeky_Squirrel	P4_2600	160000	4600000		-		-	-	0.038	-	-	3.136%
2015-11-19T06:48:33	Alexander Dubrovin	Manual testing	1000000	5000000	6	-		-	-	0.116	-	-	3.982%
2015-11-19T06:48:33	Alexander Dubrovin	Manual testing	1500000	6000000	6	-		-	-	0.166	-	-	4.273%
2015-12-19T14:31:21	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.033%

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	-	-
2009-01-11T04:33:00	Sturle Sunde	ginjtje.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-18T20:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.138	-	-
2013-08-20T11:14:00	David Campeau	Manual testing	2⁶²	2⁶³		-	-	0.442	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.884	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.683	-	-
2015-10-23T09:34:53	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.366	-	-
2016-12-24T00:00:57	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.733	-	-
2019-04-22T13:11:39	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.47	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.400 GHz-days
Estimated T-Level:	3.150

Digits	B1	Curves	Complete	FacMiss
20	11000	63 / 100	0.630	53.091%
25	50000	63 / 280	0.225	79.819%

New Calculation Method

Total ECM effort:	5.400 GHz-days
Estimated T-Level:	3.150

Digits	B1	Complete	FacMiss
20	11000	2.032	13.104%
25	50000	0.184	83.221%
30	250000	0.011	98.875%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	5.143
50000	5000000	109660552183222375915807	3	0.257

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-09T02:08:00	S36049	Wolle3	50000	5000000						3	0.257
2009-12-19T07:38:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.257
2011-09-25T01:27:00	Huaiyu Wu	lenovo	50000	5000000						3	0.257
2013-06-09T06:18:00	jim f in mn	asus	50000	5000000						3	0.257
2015-03-17T19:03:00	Bruce	desk16	50000	5000000						3	0.257
2016-03-16T17:30:41	Bruce	Desk6	50000	5000000						3	0.257
2016-03-28T20:30:15	James P McMillan	caturday	50000	5000000						3	0.257
2016-07-06T21:20:53	Bruce	Desk6	50000	5000000						3	0.257
2016-11-19T19:58:07	NBCC		50000	5000000						3	0.257
2017-05-13T05:00:47	Bruce	Desk6	50000	5000000						3	0.257
2017-11-22T20:51:46	Bruce	Desk6	50000	5000000						3	0.257
2018-04-14T02:22:27	Bruce	Desk6	50000	5000000						3	0.257
2018-10-12T00:43:32	Bruce	Desk6	50000	5000000						3	0.257
2020-02-12T00:12:13	David_McCann	i5	50000	5000000						3	0.257
2020-02-18T03:31:54	mnd9	50869b	50000	5000000						3	0.257
2020-02-25T07:49:42	EricP	Cannonfodder	50000	5000000						3	0.257
2020-03-03T11:42:31	MarkS	desktop-i7	50000	5000000						3	0.257
2020-03-09T17:11:16	mnd9	50869b	50000	5000000						3	0.257
2020-03-17T16:37:59	kracker	O0	50000	5000000						3	0.257
2020-03-28T00:14:46	kracker	O0	50000	5000000						3	0.257
2020-04-08T18:45:00	daveward2005	MW	50000	5000000	109660552183222375915807	76.537	3	2		3	0.257

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	5F6C2D3AFA0604F2	0.146
2018-04-18T19:26:09	kkmrkkblmbrbk	old	5F6C2D3AFA0604F2	0.146

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 = 65000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1500000, B2 = 6000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 1000000, B2 = 5000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 160000, B2 = 4600000 (P-1 stage 2)

B1 = 85000, B2 = 1593750 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 142828 (P-1 stage 1)

B1 = 113914 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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