M2188231 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	27.2388	67.6471%	2500000	125000000	0.8746	7.9308%	28.1135	70.2129%	2.5659%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8603%	0.0194	63.1539%	1.0849%
GPU72	2⁶²	0.2808	64.5161%	11000	160000	0.0018	1.5699%	0.2826	65.0732%	0.5571%
Difference	+6	+26.9581	+3.1309%	+2489000	+124840000	+0.8728	+6.3609%	+27.8309	+5.1397%	+5.1397%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2188231	1100324412318467545923719	25	79.864	251418705867540389 251418705867540389	2020-05-04	1	251418705867540389	79,554	1.306e+9	2.439e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.355%
2011-01-12T17:30:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.205%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	119332	119332		-		-	-	0.011	-	-	0.890%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148664	148664		-		-	-	0.014	-	-	1.007%
2016-02-13T08:02:49	Jocelyn Larouche	Manual testing	442491	4424910	6	-		-	-	0.063	-	-	3.588%
2018-02-22T01:34:48	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.931%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	Stephen Wood	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-02T22:28:00	Sturle Sunde	ginjtje.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T08:45:00	Sturle Sunde	fungo.ifi	2⁶¹	2⁶²		-	-	0.140	-	-
2013-12-03T17:40:00	LaurV	Manual testing	2⁶²	2⁶³		-	-	0.449	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.897	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.707	-	-
2016-01-02T13:51:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.415	-	-
2016-11-24T19:46:06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.830	-	-
2019-04-15T13:43:08	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.66	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.331 GHz-days
Estimated T-Level:	3.700

Digits	B1	Curves	Complete	FacMiss
20	11000	74 / 100	0.740	47.534%
25	50000	74 / 280	0.264	76.739%

New Calculation Method

Total ECM effort:	6.331 GHz-days
Estimated T-Level:	3.700

Digits	B1	Complete	FacMiss
20	11000	2.387	9.190%
25	50000	0.216	80.594%
30	250000	0.013	98.680%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		72	6.160
50000	5000000	1100324412318467545923719	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-22T08:35:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.257
2009-12-11T04:17:00	James Hintz	ryan	50000	5000000						3	0.257
2011-09-30T09:06:00	Lukasz Wrobel	i-2	50000	5000000						3	0.257
2013-05-18T07:00:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-04T23:39:00	Jason U	Server7	50000	5000000						3	0.257
2015-12-12T05:18:17	guru	w1	50000	5000000						3	0.257
2016-03-07T13:30:30	Jason U	Server7	50000	5000000						3	0.257
2016-06-26T20:46:13	Bruce	Desk6	50000	5000000						3	0.257
2016-11-03T18:21:48	Bruce	Desk6	50000	5000000						3	0.257
2017-04-15T20:00:19	Bruce	Desk6	50000	5000000						3	0.257
2017-11-04T08:19:24	Conductor	Sasha	50000	5000000						3	0.257
2018-03-18T14:49:00	Bruce	Desk6	50000	5000000						3	0.257
2018-09-11T14:45:24	Bruce	Desk6	50000	5000000						3	0.257
2020-01-29T23:26:47	Nesowa	entropy_generator_2	50000	5000000						3	0.257
2020-02-07T14:12:44	Keysarecool	i9	50000	5000000						3	0.257
2020-02-15T17:34:12	mnd9	colab2	50000	5000000						3	0.257
2020-02-23T02:04:56	mnd9	libproj	50000	5000000						3	0.257
2020-03-01T11:07:10	Corey	Computer	50000	5000000						3	0.257
2020-03-06T12:30:39	mat10243x	K3	50000	5000000						3	0.257
2020-03-14T03:02:12	mnd9	75201b	50000	5000000						3	0.257
2020-03-21T17:26:42	mnd9	l2lounge	50000	5000000						3	0.257
2020-04-03T00:10:38	EricP	Cannonfodder	50000	5000000						3	0.257
2020-04-17T12:54:27	mnd9	libproj	50000	5000000						3	0.257
2020-04-26T13:39:35	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.257
2020-05-04T17:50:10	daveward2005	Davy	50000	5000000	1100324412318467545923719	79.864	2	2		2	0.171

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	Stephen Wood	v4_computers	2C1F292D9131578C	0.144
2018-04-14T16:20:14	kkmrkkblmbrbk	old	2C1F292D9131578C	0.144

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 442491, B2 = 4424910 (P-1 stage 2)

B1 = 442491 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148664 (P-1 stage 1)

B1 = 119332 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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