M2223853 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	26.8025	67.6471%	2000000	65000000	0.5179	7.0347%	27.3204	69.9230%	2.2759%
PrimeNet	2⁵⁸	0.0173	62.0690%	10000	180000	0.0018	2.8688%	0.0191	63.1571%	1.0882%
GPU72	2⁶²	0.2763	64.5161%	11000	180000	0.0019	1.6305%	0.2782	65.0947%	0.5785%
Difference	+6	+26.5263	+3.1309%	+1989000	+64820000	+0.5160	+5.4042%	+27.0423	+4.8283%	+4.8283%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2223853	541770638078232941471	21	68.876	121809004029995 5 × 19² × 31 × 2176910089	2020-07-01	361	2176910089	50.397	11.307	21.119

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%
2010-10-21T04:11:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.675%
2011-01-12T21:12:00	Oscar Östlin		85000	1593750		-		-	-	0.016	-	-	2.176%
2014-05-26T23:57:00	Jocelyn Larouche	Manual testing	113862	113862		-		-	-	0.011	-	-	0.869%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	142724	142724		-		-	-	0.014	-	-	0.987%
2015-05-02T13:30:00	Squeeky_Squirrel	P4_2600	160000	4600000		-		-	-	0.038	-	-	3.137%
2015-11-21T11:26:55	Alexander Dubrovin	Manual testing	1000000	5000000	6	-		-	-	0.116	-	-	3.983%
2015-12-22T07:19:43	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.035%

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	-	-
2016-02-23T16:29:09	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-11T14:17:00	Sturle Sunde	buxtehude.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-19T07:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.138	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.441	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.883	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.680	-	-
2015-10-25T20:35:08	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.360	-	-
2016-12-24T00:00:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.721	-	-
2019-04-22T13:11:38	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.44	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.944 GHz-days
Estimated T-Level:	4.050

Digits	B1	Curves	Complete	FacMiss
20	11000	81 / 100	0.810	44.305%
25	50000	81 / 280	0.289	74.841%

New Calculation Method

Total ECM effort:	6.944 GHz-days
Estimated T-Level:	4.050

Digits	B1	Complete	FacMiss
20	11000	2.613	7.332%
25	50000	0.236	78.966%
30	250000	0.015	98.556%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		79	6.773
50000	5000000	541770638078232941471	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-12T00:45:00	bayanne	MacBook	50000	5000000						3	0.257
2009-12-24T10:45:00	Lukasz Wrobel	cm-3	50000	5000000						3	0.257
2011-09-26T02:58:00	Bud	annan	50000	5000000						3	0.257
2013-06-13T13:13:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-19T09:02:00	Bruce	desk16	50000	5000000						3	0.257
2015-12-23T12:14:48	Alexander Dubrovin	Manual testing	50000	5000000						3	0.257
2016-03-18T03:06:51	Bruce	Desk6	50000	5000000						3	0.257
2016-07-08T00:35:08	lettp	Home	50000	5000000						3	0.257
2016-11-23T00:16:32	Bruce	Desk6	50000	5000000						3	0.257
2017-01-24T23:30:16	Alexander Dubrovin	Manual testing	50000	5000000						1	0.086
2017-08-11T00:51:40	Bruce	Desk6	50000	5000000						3	0.257
2018-01-07T01:10:34	Bruce	Desk6	50000	5000000						3	0.257
2018-06-28T09:15:25	Bruce	Desk6	50000	5000000						3	0.257
2019-08-11T20:51:50	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2020-02-14T20:28:26	daveward2005	Davy	50000	5000000						3	0.257
2020-02-22T06:27:24	EricP	Cannonfodder	50000	5000000						3	0.257
2020-02-28T16:32:24	EricP	Cannonfodder	50000	5000000						3	0.257
2020-03-06T06:31:46	mnd9	l2lounge	50000	5000000						3	0.257
2020-03-13T19:44:11	kracker	O0	50000	5000000						3	0.257
2020-03-21T12:10:04	kracker	O0	50000	5000000						3	0.257
2020-04-06T07:34:23	raff	mini	50000	5000000						3	0.257
2020-04-16T07:45:06	Keysarecool	HPLaptop	50000	5000000						3	0.257
2020-04-25T22:58:50	nordi	sweet16	50000	5000000						3	0.257
2020-05-04T03:18:20	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2020-05-15T13:25:21	daveward2005	Davy	50000	5000000						3	0.257
2020-06-01T18:28:17	daveward2005	Davy	50000	5000000						3	0.257
2020-06-21T19:14:34	mnd9	touchdown	50000	5000000						3	0.257
2020-07-01T04:45:33	MarkS	desktop-i7	50000	5000000	541770638078232941471	68.876	2	2	8735203820829675	2	0.171

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	ED21DEAB4A0C8433	0.146
2018-04-19T11:25:09	kkmrkkblmbrbk	old	ED21DEAB4A0C8433	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 = 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 = 142724 (P-1 stage 1)

B1 = 113862 (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

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