M2209421 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	26.9776	67.6471%	5000000	200000000	1.4896	8.9605%	28.4672	70.5461%	2.8990%
PrimeNet	2⁵⁸	0.0174	62.0690%	10000	180000	0.0018	2.8653%	0.0192	63.1558%	1.0869%
GPU72	2⁶²	0.2781	64.5161%	11000	170000	0.0019	1.6014%	0.2799	65.0844%	0.5682%
Difference	+6	+26.6995	+3.1309%	+4989000	+199830000	+1.4877	+7.3591%	+28.1872	+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
2209421	250687111624715638623239	24	77.730	56731404206060239 79 × 718119040583041	2020-04-25	79	718119040583041	20,208	3,730,090	6,966,769

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-16T01:59:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.515%
2012-01-07T02:01:00	Squeeky_Squirrel	P4_2600	135000	2733750		-		-	-	0.026	-	-	2.708%
2015-11-11T05:09:37	Alexander Dubrovin	Manual testing	1000000	2500000	6	-		-	-	0.103	-	-	3.303%
2015-12-08T16:57:51	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%
2019-12-28T18:16:15	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
1999-04-23T00:00:00	Phantomas	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-02T08:07:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T13:47:00	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		-	-	0.889	-	-
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:	5.739 GHz-days
Estimated T-Level:	3.350

Digits	B1	Curves	Complete	FacMiss
20	11000	67 / 100	0.670	50.999%
25	50000	67 / 280	0.239	78.685%

New Calculation Method

Total ECM effort:	5.739 GHz-days
Estimated T-Level:	3.350

Digits	B1	Complete	FacMiss
20	11000	2.161	11.518%
25	50000	0.195	82.256%
30	250000	0.012	98.804%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		66	5.653
50000	5000000	250687111624715638623239	1	0.086

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-10T01:07:00	Matt	Dell	50000	5000000						3	0.257
2009-12-16T01:53:00	James Hintz	ryan	50000	5000000						3	0.257
2011-09-14T07:43:00	Bud	annan	50000	5000000						3	0.257
2013-06-02T16:29:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-20T01:32:00	S36049	Wolle6	50000	5000000						3	0.257
2016-01-21T15:52:48	Jason U	Server7	50000	5000000						3	0.257
2016-03-13T17:25:32	Jason U	Server7	50000	5000000						3	0.257
2016-09-01T08:45:28	Bruce	Desk6	50000	5000000						3	0.257
2016-11-17T03:11:11	NBCC		50000	5000000						3	0.257
2017-05-02T01:05:21	Bruce	Desk6	50000	5000000						3	0.257
2017-11-15T05:02:46	J.R. Allen	lapacer	50000	5000000						3	0.257
2018-04-03T11:14:04	Bruce	Desk6	50000	5000000						3	0.257
2018-10-06T08:25:01	Bruce	Desk6	50000	5000000						3	0.257
2020-02-07T12:40:01	Alvin Bunk	BADCAT	50000	5000000						3	0.257
2020-02-15T00:44:50	mnd9	office2	50000	5000000						3	0.257
2020-02-22T16:19:04	mnd9	75211backdoorb	50000	5000000						3	0.257
2020-03-08T23:14:27	Nesowa	6700T	50000	5000000						3	0.257
2020-03-14T00:01:21	Alvin Bunk	BADCAT	50000	5000000						3	0.257
2020-03-21T13:12:14	mnd9	office2	50000	5000000						3	0.257
2020-04-06T17:58:23	kracker	O0	50000	5000000						3	0.257
2020-04-16T11:30:01	mnd9	eileen	50000	5000000						3	0.257
2020-04-26T03:48:09	mnd9	25836b	50000	5000000	250687111624715638623239	77.730	1	2	5376048379017896	1	0.086
2020-10-04T13:50:45	mnd9	75202b	50000	5000000						3	0.257

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	Phantomas	v4_computers	3C1CE517F4E9C7A1	0.145
2018-04-17T04:30:46	kkmrkkblmbrbk	old	3C1CE517F4E9C7A1	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 = 135000, B2 = 2733750 (P-1 stage 2)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

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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