M1081541 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	2⁷¹	442.0344	70.4225%	5000000	100000000	0.4373	5.8802%	442.4717	72.1617%	1.7392%
PrimeNet	2⁵⁶	0.0089	62.5000%	4500	65000	0.0003	2.0204%	0.0092	63.2576%	0.7576%
GPU72	2⁶⁰	0.1420	65.0000%	4500	20000	0.0002	0.6529%	0.1422	65.2285%	0.2285%
Difference	+11	+441.8924	+5.4225%	+4995500	+99980000	+0.4371	+5.2273%	+442.3295	+6.9332%	+6.9332%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1081541	1932450416295351272647	22	70.711	893378252093703 3 × 11003 × 27064686967	2017-05-12	11003	27064686967	353.16	63.372	118.36

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-03T00:00:00	Jocelyn Larouche	v4_computers	15000	172500		-		-	-	0.001	-	-	0.368%
2012-01-04T12:54:00	bcp19	Toshiba-740Q	200000	10000000		-		-	-	0.032	-	-	2.486%
2012-02-06T19:26:00	bcp19	Toshiba-740Q	200000	100000000		-		-	-	0.242	-	-	3.738%
2014-08-21T02:33:00	Jocelyn Larouche	Manual testing	259345	259345		-		-	-	0.011	-	-	0.808%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	318690	318690		-		-	-	0.014	-	-	0.904%
2014-11-24T11:45:00	BloodIce	URM2	1000000	1000000		-		-	-	0.043	-	-	1.565%
2014-11-24T19:10:00	BloodIce	URM2	5000000	100000000		-		-	-	0.437	-	-	5.880%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.018	-	-
2016-02-23T16:28:21	Mark Rose	Manual testing	2⁵⁷	2⁶⁰		-	-	0.124	-	-
2009-02-25T19:36:00	Sturle Sunde	czerny.ifi	2⁶⁰	2⁶¹		-	-	0.142	-	-
2010-11-16T04:34:00	Michael C	Manual testing	2⁶¹	2⁶²		-	-	0.284	-	-
2012-10-18T21:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.908	-	-
2014-02-02T14:51:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	1.815	-	-
2014-02-03T00:40:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	3.455	-	-
2014-02-22T13:30:00	Never Odd Or Even	Manual testing	2⁶⁵	2⁶⁶		-	-	6.909	-	-
2014-02-22T13:31:00	Never Odd Or Even	Manual testing	2⁶⁶	2⁶⁷		-	-	13.82	-	-
2014-02-22T13:31:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	27.64	-	-
2014-02-22T13:31:00	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	55.27	-	-
2014-02-22T13:31:00	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰		-	-	110.5	-	-
2014-04-01T16:48:00	Never Odd Or Even	Manual testing	2⁷⁰	2⁷¹	MISSED FACTOR!	-	-	221.1	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.758 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	18.758 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.727	0.000%
25	50000	1.369	25.440%
30	250000	0.110	89.563%
35	1000000	0.007	99.278%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		246	8.639
50000	5000000	1932450416295351272647	31	1.089
50000	12746599		3	0.166
250000	35000000		44	8.865

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-28T04:24:00	James Heinrich	WHS	50000	5000000						1	0.035
2008-03-27T04:54:00	arnaud	CITRIX2K	50000	5000000						3	0.105
2008-12-08T02:35:00	Sturle Sunde	v23	50000	5000000						3	0.105
2009-04-21T20:16:00	Sturle Sunde	v23	50000	5000000						3	0.105
2009-08-25T14:36:00	ANONYMOUS	mpow	50000	5000000						3	0.105
2009-08-25T15:46:00	ANONYMOUS	mpow	50000	5000000						3	0.105
2010-04-09T10:35:00	sannerud.com	snap2	50000	5000000						3	0.105
2010-12-12T02:10:00	Nguyen Xuan Khanh	khanhnx	50000	5000000						3	0.105
2011-06-02T07:19:00	maxybo	CB418E216	50000	5000000						3	0.105
2012-01-26T03:09:00	Pool Party	sts	50000	5000000						3	0.105
2012-08-14T07:52:00	soldake		50000	5000000						3	0.105
2013-02-08T15:28:00	Pool Party	sts	50000	5000000						3	0.105
2013-06-13T20:27:00	Pool Party	sts	50000	5000000						3	0.105
2013-09-19T19:19:00	561	561	50000	5000000						3	0.105
2014-03-09T12:44:00	Bruce	snowflake	50000	5000000						3	0.105
2014-08-01T18:05:00	Xyzzy	jv	50000	5000000						3	0.105
2015-03-03T00:14:00	OS1	Tina	50000	5000000						3	0.105
2015-04-28T12:44:00	OS1	Tina	50000	5000000						3	0.105
2015-07-29T16:38:00	OS1	Tina	50000	5000000						3	0.105
2015-11-03T07:08:44	arnaud	ATTAX15	50000	5000000						3	0.105
2016-02-01T09:15:13	arnaud	ATTAX13	50000	5000000						3	0.105
2016-04-06T14:42:32	raman22feb1988	Manual testing	50000	12746599						3	0.166
2016-04-23T15:22:03	raman22feb1988	Suganya	50000	5000000						3	0.105
2016-05-18T00:00:00	Bruce	Desk9	50000	5000000						3	0.105
2016-06-28T10:24:50	raman22feb1988	Alex_Pandian	50000	5000000						3	0.105
2016-09-01T13:09:47	raman22feb1988	Nithya	50000	5000000						3	0.105
2016-12-24T10:57:01	raman22feb1988	Alex_Pandian	50000	5000000						3	0.105
2017-04-15T20:41:59	driveByUpgrades	AMD8	50000	5000000						3	0.105
2017-05-12T15:32:46	TJAOI	Manual testing	50000	5000000						32	1.124
2017-05-12T15:32:46	TJAOI	Manual testing	50000	5000000	1932450416295351272647	70.711	31	2		31	1.089
2018-01-05T12:40:08	TJAOI	Manual testing	50000	5000000						135	4.741
2021-04-09T16:09:08	TJAOI	Manual testing	250000	35000000						44	8.865

date	userid	compid	res64	spent (GHz-days)
2003-12-13T00:00:00	ANONYMOUS	v4_computers	74CBC28099058383	0.032
2016-06-01T18:47:41	MadPoo	Manual testing	74CBC28099058383	0.032

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 = 100000000 (P-1 stage 2)

B1 = 200000, B2 = 100000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 200000, B2 = 10000000 (P-1 stage 2)

B1 = 318690 (P-1 stage 1)

B1 = 259345 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 15000, B2 = 172500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

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10¹⁰

10¹¹

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