M2188481 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	2⁶⁹	54.5524	68.1159%	2500000	125000000	0.8746	7.3041%	55.4270	70.4448%	2.3289%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8603%	0.0194	63.1539%	1.0849%
GPU72	2⁶²	0.2807	64.5161%	11000	160000	0.0018	1.5700%	0.2825	65.0732%	0.5571%
Difference	+7	+54.2716	+3.5998%	+2489000	+124840000	+0.8728	+5.7342%	+55.1444	+5.3716%	+5.3716%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2188481	2949136590706877760915353	25	81.287	673786199356283596 2² × 11 × 15313322712642809	2021-11-29	11	15313322712642809	285,583	79,541,227	148,560,860

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	-	-	0.182%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.165%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.300%
2011-01-12T15:55:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	1.951%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	119328	119328		-		-	-	0.011	-	-	0.773%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148656	148656		-		-	-	0.014	-	-	0.878%
2016-02-13T08:02:49	Jocelyn Larouche	Manual testing	442455	4424550	6	-		-	-	0.063	-	-	3.235%
2018-02-23T07:46:23	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.304%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-03T01:48:00	Sturle Sunde	ginjtje.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T15:22:00	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		-	-	6.829	-	-
2019-04-15T13:43:08	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.66	-	-
2021-07-15T09:28:00	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	27.32	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.091 GHz-days
Estimated T-Level:	23.339

Digits	B1	Curves	Complete	FacMiss
20	11000	187 / 100	1.870	15.268%
25	50000	187 / 280	0.668	51.219%

New Calculation Method

Total ECM effort:	16.091 GHz-days
Estimated T-Level:	23.339

Digits	B1	Complete	FacMiss
20	11000	6.055	0.235%
25	50000	0.547	57.865%
30	250000	0.034	96.687%
35	1000000	0.002	99.846%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		168	14.37
50000	5000000	2949136590706877760915353	5	0.428
50000	5150000		7	0.606
50000	6750000		7	0.685

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-26T13:43:00	Smurgs	Praca	50000	5000000						3	0.257
2009-12-11T03:49:00	SubPrime	abd0	50000	5000000						3	0.257
2011-09-02T21:11:00	Bud	annan	50000	5000000						3	0.257
2013-05-20T13:41:00	hiems	Laptop	50000	5000000						3	0.257
2015-03-05T05:31:00	Jason U	Server7	50000	5000000						3	0.257
2015-12-12T10:12:26	guru	w1	50000	5000000						3	0.257
2016-03-07T20:27:25	Bruce	Desk6	50000	5000000						3	0.257
2016-06-29T02:32:34	Bruce	test	50000	5000000						3	0.257
2016-11-04T03:56:12	Bruce	Desk6	50000	5000000						3	0.257
2017-04-16T01:17:32	Bruce	Desk6	50000	5000000						3	0.257
2017-11-04T12:14:05	Bruce	Desk6	50000	5000000						3	0.257
2018-03-18T20:19:10	Bruce	Desk6	50000	5000000						3	0.257
2018-09-11T19:56:47	Bruce	Desk6	50000	5000000						3	0.257
2020-01-29T15:13:30	David_McCann	i5	50000	5000000						3	0.257
2020-02-08T02:36:09	David_McCann	i5	50000	5000000						3	0.257
2020-02-15T18:01:08	mnd9	libproj	50000	5000000						3	0.257
2020-02-23T02:47:39	Sergey Nosov	TS140-02	50000	5000000						3	0.257
2020-02-29T06:28:09	MarkS	desktop-i7	50000	5000000						3	0.257
2020-03-06T16:10:49	MarkS	laptop64	50000	5000000						3	0.257
2020-03-14T01:53:23	mnd9	office2	50000	5000000						3	0.257
2020-03-21T20:36:41	EricP	Cannonfodder	50000	5000000						3	0.257
2020-04-17T15:03:16	Yxinity	Olga	50000	5000000						3	0.257
2020-04-26T13:24:56	SXS2297	M-Laptop	50000	5000000						3	0.257
2020-04-26T19:05:24	mnd9	50871b	50000	5000000						3	0.257
2020-05-05T08:31:55	mnd9	50871b	50000	5000000						3	0.257
2020-05-17T01:23:49	mnd9	50871b	50000	5000000						3	0.257
2020-06-03T02:53:41	Summy	CHB	50000	5000000						3	0.257
2020-06-22T07:37:43	Nesowa	6700T	50000	5000000						3	0.257
2020-07-01T19:47:23	IanGlencross	glenx24	50000	5000000						3	0.257
2020-07-08T12:48:07	GAN	OSK-L2	50000	5000000						3	0.257
2020-07-14T11:19:45	GAN	LMS-01	50000	5000000						3	0.257
2020-07-20T18:34:51	daveward2005	Dave2	50000	5000000						3	0.257
2020-07-27T05:00:23	daveward2005	Dave2	50000	5000000						3	0.257
2020-08-03T09:01:59	GAN	LMS-06	50000	5000000						3	0.257
2020-08-11T05:00:38	GAN	LMS-16	50000	5000000						3	0.257
2020-08-27T20:17:18	MarkS	laptop64	50000	5000000						7	0.599
2020-09-30T13:16:28	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.599
2020-10-26T15:58:03	lycorn	colab_S	50000	5000000						7	0.599
2020-12-01T12:32:06	daveward2005	Dave2	50000	5000000						7	0.599
2021-01-04T05:35:00	daveward2005	Dave2	50000	5000000						7	0.599
2021-02-03T19:11:27	RIHATEC	i7-3770K	50000	5000000						7	0.599
2021-03-04T14:11:02	Deufo	Ryzen2600	50000	6750000						7	0.685
2021-04-15T14:55:26	Zenzoma	AMD3970X	50000	5000000						7	0.599
2021-06-07T10:43:50	kutens	sol	50000	5150000						7	0.606
2021-07-18T01:35:05	tottenhoff	Garage-Band-003	50000	5000000						7	0.599
2021-09-09T03:41:08	EthanD	LexxBuntu	50000	5000000						7	0.599
2021-11-29T04:17:54	daveward2005	d12436	50000	5000000	2949136590706877760915353	81.287	5	2	5157644745846970	5	0.428

date	userid	compid	res64	spent (GHz-days)
1997-12-30T00:00:00	ANONYMOUS	v4_computers	5D8FEB2533E52A92	0.144
1999-07-12T00:00:00	ANONYMOUS	v4_computers	5D8FEB2533E52A92	0.144
2018-04-14T17:25:41	kkmrkkblmbrbk	old	5D8FEB2533E52A92	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 = 442455, B2 = 4424550 (P-1 stage 2)

B1 = 442455 (P-1 stage 1)

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

B1 = 148656 (P-1 stage 1)

B1 = 119328 (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)

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10¹⁷

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