M2179729 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	27.3451	67.6471%	2500000	125000000	0.8746	7.9277%	28.2197	70.2119%	2.5649%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8582%	0.0195	63.1531%	1.0841%
GPU72	2⁶²	0.2819	64.5161%	11000	160000	0.0018	1.5687%	0.2837	65.0728%	0.5566%
Difference	+6	+27.0632	+3.1309%	+2489000	+124840000	+0.8728	+6.3590%	+27.9361	+5.1392%	+5.1392%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2179729	7082523432907837660533863	25	82.551	1624633941400017539 23 × 139 × 1373 × 370119825419	2020-11-20	1373	370119825419	478,434	1,922.5	3,590.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-05T01:17:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-08T11:36:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.354%
2011-01-14T09:46:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.204%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	119446	119446		-		-	-	0.011	-	-	0.890%
2014-10-07T22:12:00	Jocelyn Larouche	Manual testing	148892	148892		-		-	-	0.014	-	-	1.007%
2016-01-04T02:12:25	Jocelyn Larouche	Manual testing	443655	4436550	6	-		-	-	0.063	-	-	3.589%
2018-01-20T00:52:25	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.928%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
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	-	-
2009-01-04T10:32:00	Sturle Sunde	fungo.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-07T01:57:00	Sturle Sunde	dietrich.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.450	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.901	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.714	-	-
2016-01-02T13:50:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.428	-	-
2016-11-24T19:46:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.857	-	-
2019-04-22T13:11:41	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.71	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.859 GHz-days
Estimated T-Level:	22.268

Digits	B1	Curves	Complete	FacMiss
20	11000	127 / 100	1.270	27.904%
25	50000	127 / 280	0.454	63.484%

New Calculation Method

Total ECM effort:	10.859 GHz-days
Estimated T-Level:	22.268

Digits	B1	Complete	FacMiss
20	11000	4.097	1.663%
25	50000	0.370	69.055%
30	250000	0.023	97.746%
35	1000000	0.001	99.896%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		126	10.77
50000	5000000	7082523432907837660533863	1	0.086

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-12T09:43:00	Dalos Lee	dalosdesk	50000	5000000						3	0.257
2009-12-07T08:21:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.257
2011-08-30T16:09:00	S36049	Wolle5	50000	5000000						3	0.257
2013-05-15T14:51:00	ANONYMOUS		50000	5000000						3	0.257
2015-02-26T15:06:00	arnaud	CHAMOT22	50000	5000000						3	0.257
2015-12-19T02:57:51	dragon325	Falken-i7-920	50000	5000000						3	0.257
2016-03-06T05:21:32	Bruce	Desk6	50000	5000000						3	0.257
2016-06-23T23:58:56	Bruce	Desk6	50000	5000000						3	0.257
2016-10-25T21:55:30	Bruce	Desk6	50000	5000000						3	0.257
2017-04-08T17:24:59	Bruce	Desk6	50000	5000000						3	0.257
2017-11-01T23:09:11	Bruce	Desk6	50000	5000000						3	0.257
2018-03-11T13:12:40	Bruce	Desk6	50000	5000000						3	0.257
2018-08-27T03:20:28	Bruce	Desk6	50000	5000000						3	0.257
2020-02-05T00:12:21	ANONYMOUS		50000	5000000						3	0.257
2020-02-12T09:42:45	Keysarecool	i9	50000	5000000						3	0.257
2020-02-19T14:06:33	IanGlencross	glenx24	50000	5000000						3	0.257
2020-02-26T22:17:27	Nesowa	6700T	50000	5000000						3	0.257
2020-03-04T10:59:43	Keysarecool	HPLaptop	50000	5000000						3	0.257
2020-03-11T06:14:51	Sergey Nosov	TS140-02	50000	5000000						3	0.257
2020-03-18T11:58:43	MarkS	laptop64	50000	5000000						3	0.257
2020-03-27T15:46:29	Alvin Bunk	BADCAT	50000	5000000						3	0.257
2020-03-30T03:12:37	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2020-04-11T02:55:02	daveward2005	Davy	50000	5000000						3	0.257
2020-04-23T12:47:49	mnd9	25836b	50000	5000000						3	0.257
2020-04-30T20:42:32	nordi	sweet16	50000	5000000						3	0.257
2020-05-11T22:24:41	nordi	sweet16	50000	5000000						3	0.257
2020-05-28T05:44:14	mnd9	kitchen	50000	5000000						3	0.257
2020-06-15T01:21:21	GAN	LMS-17	50000	5000000						3	0.257
2020-06-29T01:54:27	GAN	AC-KL	50000	5000000						3	0.257
2020-07-05T17:48:56	GAN	LMS-16	50000	5000000						3	0.257
2020-07-12T21:50:56	lycorn	colab_ES	50000	5000000						3	0.257
2020-07-20T20:46:59	mnd9	office2	50000	5000000						3	0.257
2020-07-25T01:25:20	GAN	OSK-SCH03	50000	5000000						3	0.257
2020-07-31T08:35:28	GAN	LMS-12	50000	5000000						3	0.257
2020-08-08T18:00:12	Brett Walker	brain	50000	5000000						3	0.257
2020-08-16T23:48:53	M. R. Mayer	nimbus	50000	5000000						7	0.599
2020-09-18T17:07:11	mnd9	f4b	50000	5000000						7	0.599
2020-10-17T17:33:45	tottenhoff	4-of-4-Ryzen-5-3600	50000	5000000						7	0.599
2020-11-20T05:14:24	daveward2005	Dave2	50000	5000000	7082523432907837660533863	82.551	1	2	8232719199031258	1	0.086

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	007301455DACC800	0.143
2018-04-13T12:56:21	kkmrkkblmbrbk	old	007301455DACC800	0.143

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 = 443655, B2 = 4436550 (P-1 stage 2)

B1 = 443655 (P-1 stage 1)

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

B1 = 148892 (P-1 stage 1)

B1 = 119446 (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)

10²

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10¹⁰

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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