M822721 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	2⁶⁷	36.1166	70.1493%	8227210	246816300	0.6147	9.3905%	36.7313	72.9524%	2.8031%
PrimeNet	2⁴⁰	0.0000	50.0000%	8000	320000	0.0007	22.7539%	0.0007	61.3769%	11.3769%
GPU72	2⁴⁴	0.0000	54.5455%	14000	550000	0.0013	17.5060%	0.0013	62.5027%	7.9573%
Difference	+23	+36.1166	+15.6038%	+8213210	+246266300	+0.6135	-8.1155%	+36.7301	+10.4497%	+10.4497%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
822721	387969366090471501142361	24	78.360	235784285371633580 2² × 5 × 11789214268581679	2016-06-16	5	11789214268581679	125,945	18,601,088	34,741,652

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.205%
2002-02-10T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.438%
2002-04-07T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.789%
2002-05-18T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.280%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.919%
2002-11-24T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.698%
2003-07-21T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.605%
2008-10-26T22:45:00	markr	Manual testing	1000000	20000000		-		-	-	0.059	-	-	5.253%
2008-10-29T23:36:00	markr	Manual testing	1000000	40000000		-		-	-	0.090	-	-	5.951%
2012-09-21T00:59:00	Jocelyn Larouche	Manual testing	1645442	1645442		-		-	-	0.048	-	-	2.836%
2013-11-02T05:09:00	David Campeau	i5-2500k	1670000	56780000		-		-	-	0.135	-	-	6.643%
2015-11-26T02:15:34	Sid & Andy	Hand_In_The_Box	8227210	246816300	12	-		-	-	0.615	-	-	9.390%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-02-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.023	-	-
2003-08-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.047	-	-
2008-10-14T05:25:00	Sturle Sunde	aeronca.ifi	2⁵⁸	2⁵⁹		-	-	0.047	-	-
2008-10-14T06:01:00	Sturle Sunde	aeronca.ifi	2⁵⁹	2⁶⁰		-	-	0.093	-	-
2010-06-01T02:20:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.187	-	-
2015-02-27T10:10:00	TJAOI	Manual testing	2⁶¹	2⁶²		-	-	0.373	-	-
2015-09-28T01:02:15	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.193	-	-
2015-09-28T01:02:15	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.386	-	-
2016-02-23T08:31:35	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	4.541	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.744 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	293 / 100	2.930	5.262%
25	50000	293 / 280	1.046	35.053%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	10.744 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	13.577	0.000%
25	50000	1.506	22.183%
30	250000	0.124	88.310%
35	1000000	0.008	99.163%

ECM Summary

B1	B2	factor	curves	GHz-days
		387969366090471501142361	1	0.00000e+0
50000	5000000		249	5.704
250000	25000000		44	5.040

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-03T10:58:00	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-21T18:11:00	Steve Scott	Abit-2	50000	5000000						3	0.069
2008-10-02T01:32:00	Sturle Sunde	v21	50000	5000000						3	0.069
2009-01-18T06:01:00	Sturle Sunde	v23	50000	5000000						3	0.069
2009-04-01T03:53:00	Sturle Sunde	v21	50000	5000000						3	0.069
2009-07-24T06:51:00	JimBa	Dmansrvr	50000	5000000						3	0.069
2009-10-01T08:38:00	SubPrime	c2d0	50000	5000000						3	0.069
2010-06-01T23:55:00	unconnected	xp-lm	50000	5000000						3	0.069
2010-06-07T23:24:00	unconnected	can-01	50000	5000000						3	0.069
2010-10-21T11:24:00	greensinoz	giopa01	50000	5000000						3	0.069
2011-01-21T18:18:00	arnaud	Arnaud-PC	50000	5000000						3	0.069
2011-10-06T22:46:00	Lukasz Wrobel	4_core_L	50000	5000000						3	0.069
2012-01-08T21:02:00	alpertron	core2quad	50000	5000000						3	0.069
2012-07-29T00:04:00	alpertron	core2quad	50000	5000000						3	0.069
2012-12-02T13:15:00	Pyro451		50000	5000000						3	0.069
2013-02-20T13:17:00	alpertron	core2quad	50000	5000000						3	0.069
2013-04-26T11:04:00	Sara	Sara	50000	5000000						3	0.069
2013-07-06T08:58:00	gucs	echo3	50000	5000000						3	0.069
2013-09-16T18:11:00	gucs	echo3	50000	5000000						3	0.069
2013-11-29T05:11:00	gucs	echo3	50000	5000000						3	0.069
2014-02-01T20:54:00	gucs	echo3	50000	5000000						3	0.069
2014-03-14T15:33:00	gucs	echo3	50000	5000000						3	0.069
2014-04-12T14:52:00	gucs	echo3	50000	5000000						3	0.069
2014-05-10T05:47:00	gucs	echo3	50000	5000000						3	0.069
2014-11-24T01:16:00	Ryan Schulz	wenn	50000	5000000						15	0.344
2016-01-04T14:35:23	TJAOI	Manual testing	50000	5000000						15	0.344
2016-02-16T11:20:35	Oussama Kiamouche	Home	50000	5000000						3	0.069
2016-03-13T21:05:22	Oussama Kiamouche	Home	50000	5000000						3	0.069
2016-03-26T09:24:41	Luigi Morelli	rebirth	50000	5000000						3	0.069
2016-04-04T04:04:46	Luigi Morelli	rebirth	50000	5000000						3	0.069
2016-04-19T06:43:29	Luigi Morelli	rebirth	50000	5000000						3	0.069
2016-04-25T06:48:53	Luigi Morelli	rebirth	50000	5000000						3	0.069
2016-05-06T01:21:42	Luigi Morelli	rebirth	50000	5000000						3	0.069
2016-06-17T01:09:04	Oussama Kiamouche	Home	50000	5000000						3	0.069
2016-06-17T03:01:50	f0rteOC	Fortissimo			387969366090471501142361	78.360		1		1	-
2016-08-02T16:13:36	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:13:45	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:13:54	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:13:57	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:14:03	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:14:08	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:14:12	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:14:20	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:14:23	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:14:29	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:15:37	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:15:41	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:15:48	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:15:51	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2016-08-02T16:15:56	Luigi Morelli	Manual testing	50000	5000000						3	0.069
2017-08-04T10:35:04	TJAOI	Manual testing	50000	5000000						80	1.833
2019-07-26T09:07:24	TJAOI	Manual testing	250000	25000000						44	5.040

date	userid	compid	res64	spent (GHz-days)
2015-04-11T15:53:00	MadPoo	Manual testing	9699DF93AEC6F20E	0.016

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 = 8227210, B2 = 246816300 (P-1 stage 2)

B1 = 8227210 (P-1 stage 1)

B1 = 1670000, B2 = 56780000 (P-1 stage 2)

B1 = 1000000, B2 = 40000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1670000 (P-1 stage 1)

B1 = 1645442 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65537 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10⁰

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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