M822037 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	36.1467	70.1493%	1665000	56610000	0.1349	6.6371%	36.2816	72.1305%	1.9812%
PrimeNet	2⁴⁰	0.0000	50.0000%	7000	300000	0.0007	22.3766%	0.0007	61.1883%	11.1883%
GPU72	2⁴⁴	0.0000	54.5455%	14000	550000	0.0013	17.5044%	0.0013	62.5020%	7.9566%
Difference	+23	+36.1467	+15.6038%	+1651000	+56060000	+0.1337	-10.8673%	+36.2803	+9.6285%	+9.6285%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
822037	54004312298409806829511	23	75.515	32847859827726615 3² × 5 × 7² × 19 × 784052030737	2015-02-24	49	784052030737	16,713	1,237.1	2,310.5

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%
2008-10-23T07:51:00	markr	Manual testing	1000000	20000000		-		-	-	0.059	-	-	5.252%
2008-10-29T07:51:00	markr	Manual testing	1000000	40000000		-		-	-	0.090	-	-	5.951%
2012-09-21T00:58:00	Jocelyn Larouche	Manual testing	1644074	1644074		-		-	-	0.048	-	-	2.835%
2013-11-02T02:32:00	David Campeau	i5-2500k	1665000	56610000		-		-	-	0.135	-	-	6.637%

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	-	-
2001-01-08T00:00:00	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	-	-
2008-10-13T04:21:00	Sturle Sunde	aeronca.ifi	2⁵⁸	2⁵⁹		-	-	0.047	-	-
2008-10-13T04:57:00	Sturle Sunde	aeronca.ifi	2⁵⁹	2⁶⁰		-	-	0.093	-	-
2010-06-01T08:30:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.187	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.476 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.476 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	6.414
50000	5000000	54004312298409806829511	1	0.023
250000	25000000		44	5.040

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-03T10:13:00	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-21T15:01:00	Steve Scott	Abit-2	50000	5000000						3	0.069
2008-10-01T21:04:00	Sturle Sunde	v21	50000	5000000						3	0.069
2009-01-18T19:19:00	Sturle Sunde	v21	50000	5000000						3	0.069
2009-04-01T00:22:00	Sturle Sunde	v21	50000	5000000						3	0.069
2009-07-23T23:51:00	JimBa	Dmansrvr	50000	5000000						3	0.069
2009-09-29T21:14:00	JimBa	HPserv	50000	5000000						3	0.069
2010-06-02T04:45:00	Geoff Wing	GW1	50000	5000000						3	0.069
2010-06-10T21:06:00	maxybo	CB418E216	50000	5000000						3	0.069
2010-10-18T23:47:00	Boots	technomicron	50000	5000000						3	0.069
2011-01-21T14:32:00	Eric Christenson	HP_DC7900_SFF_PC	50000	5000000						3	0.069
2011-10-06T13:18:00	Lackó	Iroda_Eva	50000	5000000						3	0.069
2012-01-07T22:31:00	alpertron	core2quad	50000	5000000						3	0.069
2012-07-22T05:42:00	soldake		50000	5000000						3	0.069
2012-10-26T11:13:00	Pyro451		50000	5000000						3	0.069
2013-02-13T16:22:00	gucs	echo3	50000	5000000						3	0.069
2013-04-24T22:33:00	gucs	echo3	50000	5000000						3	0.069
2013-07-05T07:42:00	gucs	echo3	50000	5000000						3	0.069
2013-09-15T07:54:00	gucs	echo3	50000	5000000						3	0.069
2013-11-27T10:26:00	gucs	echo3	50000	5000000						3	0.069
2014-02-02T23:19:00	Ryan Schulz	wenn	50000	5000000						15	0.344
2015-02-21T10:20:00	Bruce	desk16	50000	5000000						3	0.069
2015-02-24T14:00:00	Bruce	desk16	50000	5000000	54004312298409806829511	75.515	1	2		1	0.023
2015-12-18T14:14:57	TJAOI	Manual testing	50000	5000000						23	0.527
2016-08-26T16:09:45	TJAOI	Manual testing	50000	5000000						90	2.062
2017-07-14T09:31:00	TJAOI	Manual testing	50000	5000000						91	2.085
2019-10-28T14:10:30	TJAOI	Manual testing	250000	25000000						44	5.040

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 = 1665000, B2 = 56610000 (P-1 stage 2)

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

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

B1 = 1665000 (P-1 stage 1)

B1 = 1644074 (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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10⁶

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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