M825191 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	36.0085	70.1493%	1000000	40000000	0.0905	5.9531%	36.0990	71.9263%	1.7771%
PrimeNet	2⁴⁰	0.0000	50.0000%	8000	320000	0.0007	22.7610%	0.0007	61.3805%	11.3805%
GPU72	2⁴⁴	0.0000	54.5455%	14000	550000	0.0013	17.5118%	0.0013	62.5054%	7.9599%
Difference	+23	+36.0085	+15.6038%	+986000	+39450000	+0.0892	-11.5586%	+36.0978	+9.4210%	+9.4210%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
825191	222100936584704995783387271	27	87.521	134575471972370636485 5 × 85061 × 1272547 × 248651791	2014-03-13	1272547	248651791	59,892,558	0.4272	0.7328

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	-	-	1.281%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.920%
2002-11-24T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.700%
2003-07-21T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.607%
2008-11-05T22:41:00	markr	Manual testing	1000000	40000000		-		-	-	0.090	-	-	5.953%
2014-03-13T21:34:00	mikr	BC5	1000000	40000000			222100936584704995783387271	27	87.521	0.090	0.033	0.181	5.953%
2016-03-17T18:52:25	alpertron	Manual testing	300000	10000000	12	-		-	-	0.024	-	-	3.964%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-08-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-02-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-10-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.023	-	-
2003-08-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.047	-	-
2008-10-12T15:33:00	Sturle Sunde	aeronautica.ifi	2⁵⁸	2⁵⁹		-	-	0.047	-	-
2008-10-12T16:08:00	Sturle Sunde	aeronautica.ifi	2⁵⁹	2⁶⁰		-	-	0.093	-	-
2010-06-02T04:40:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.186	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.481 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:	11.481 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		281	6.439
250000	25000000		44	5.042

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-03T14:12:00	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-21T17:33:00	Team_Bundu	bundu1	50000	5000000						3	0.069
2008-10-02T22:24:00	Sturle Sunde	v23	50000	5000000						3	0.069
2009-01-19T03:17:00	Sturle Sunde	v21	50000	5000000						3	0.069
2009-10-01T02:21:00	Lupo	yorick	50000	5000000						3	0.069
2009-10-01T03:28:00	Geoff Wing	GW1	50000	5000000						3	0.069
2009-10-17T01:24:00	JimBa	atlserv	50000	5000000						3	0.069
2010-06-02T14:19:00	Geoff Wing	GW1	50000	5000000						3	0.069
2010-06-10T21:07:00	maxybo	CB418E216	50000	5000000						3	0.069
2010-10-25T00:31:00	Boots	rchok28bo	50000	5000000						3	0.069
2011-01-23T14:30:00	arnaud	Arnaud-PC	50000	5000000						3	0.069
2011-10-13T18:45:00	Bruce	GTLT-4540GZ	50000	5000000						3	0.069
2012-01-19T23:48:00	Pool Party	sts	50000	5000000						3	0.069
2012-07-25T13:13:00	soldake		50000	5000000						3	0.069
2012-11-04T23:06:00	Pool Party	sts	50000	5000000						3	0.069
2013-02-17T08:58:00	gucs	echo3	50000	5000000						3	0.069
2013-04-29T18:23:00	Sara	Sara	50000	5000000						3	0.069
2013-07-09T23:57:00	gucs	echo3	50000	5000000						3	0.069
2013-09-22T01:42:00	gucs	echo3	50000	5000000						3	0.069
2013-12-03T04:38:00	gucs	echo3	50000	5000000						3	0.069
2014-02-03T06:37:00	gucs	echo3	50000	5000000						3	0.069
2015-12-04T11:35:19	TJAOI	Manual testing	50000	5000000						39	0.894
2016-09-09T13:51:38	TJAOI	Manual testing	50000	5000000						90	2.062
2017-02-10T18:30:25	TJAOI	Manual testing	50000	5000000						91	2.085
2019-06-14T11:48:57	TJAOI	Manual testing	250000	25000000						44	5.042

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

B1 = 1000000 (P-1 stage 1)

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

B1 = 300000, B2 = 10000000 (P-1 stage 2)

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

B1 = 300000 (P-1 stage 1)

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)

10²

10³

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10³

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10⁹

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