M2050739 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	29.0651	69.1176%	4000000	200000000	1.3994	8.7611%	30.4645	71.8233%	2.7056%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6658%	0.0204	64.7583%	0.9652%
GPU72	2⁶²	0.2996	66.1290%	9000	120000	0.0014	1.3304%	0.3010	66.5797%	0.4506%
Difference	+6	+28.7655	+2.9886%	+3991000	+199880000	+1.3980	+7.4307%	+30.1635	+5.2436%	+5.2436%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2050739	12012615541526451980584831	26	83.313	2928850414783756485 3 × 5 × 11 × 37 × 479746177687757	2020-07-11	37	479746177687757	1,262,272	2,491,922	4,654,216

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.222%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.046%
2009-05-12T20:56:00	Rob_Dee	twopc	20000	280000		-		-	-	0.003	-	-	0.893%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.350%
2011-01-04T22:09:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.508%
2011-01-26T17:04:00	James Heinrich	i7-920	135000	2868750		-		-	-	0.027	-	-	2.708%
2014-10-22T23:53:00	Jocelyn Larouche	Manual testing	166298	166298		-		-	-	0.016	-	-	1.058%
2015-10-06T15:13:08	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.123	-	-	4.664%
2019-07-02T02:22:41	BigBrother	Winston	1000000	20000000	12	-		-	-	0.194	-	-	5.318%
2019-08-13T23:55:54	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.761%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	Ethan O'Connor	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.056	-	-
2009-01-02T16:25:00	Sturle Sunde	gopher.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-03-09T06:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.150	-	-
2013-09-01T20:20:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.479	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.957	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.822	-	-
2015-11-03T10:09:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.644	-	-
2016-08-14T00:04:14	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.288	-	-
2019-03-23T09:42:42	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.58	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.333 GHz-days
Estimated T-Level:	21.964

Digits	B1	Curves	Complete	FacMiss
20	11000	110 / 100	1.100	33.103%
25	50000	110 / 280	0.393	67.465%

New Calculation Method

Total ECM effort:	9.333 GHz-days
Estimated T-Level:	21.964

Digits	B1	Complete	FacMiss
20	11000	3.548	2.877%
25	50000	0.321	72.564%
30	250000	0.020	98.045%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		108	9.163
50000	5000000	12012615541526451980584831	2	0.170

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-06T06:37:00	Matthias Eckoldt	serverSP	50000	5000000						3	0.255
2009-10-25T11:22:00	lindee	tanagra	50000	5000000						3	0.255
2011-04-05T00:29:00	Lupo	yorick	50000	5000000						3	0.255
2013-03-05T01:40:00	Donna Noble	PH2x6	50000	5000000						3	0.255
2014-03-22T09:26:00	Bruce	snowflake	50000	5000000						3	0.255
2015-07-19T11:20:00	dragon325	Falken-i7-920	50000	5000000						3	0.255
2016-02-18T23:35:38	Sintax	cloud2	50000	5000000						3	0.255
2016-05-04T08:41:10	Bruce	Desk6	50000	5000000						3	0.255
2016-07-17T07:35:49	Bruce	test	50000	5000000						3	0.255
2016-12-13T18:35:56	Bruce	Desk6	50000	5000000						3	0.255
2017-06-28T05:13:25	Bruce	Desk6	50000	5000000						3	0.255
2017-11-28T12:22:08	Bruce	Desk6	50000	5000000						3	0.255
2018-04-08T17:36:12	Bruce	Desk6	50000	5000000						3	0.255
2018-09-29T01:38:38	Bruce	Desk6	50000	5000000						3	0.255
2019-12-26T05:33:05	George Woltman	colab	50000	5000000						3	0.255
2019-12-31T00:06:52	TheJudger	myECM	50000	5000000						3	0.255
2020-01-05T13:46:14	daveward2005	MW	50000	5000000						3	0.255
2020-01-12T20:35:58	EricP	Cannonfodder	50000	5000000						3	0.255
2020-01-20T08:10:39	mnd9	75201	50000	5000000						3	0.255
2020-01-26T05:08:49	mnd9	27016b	50000	5000000						3	0.255
2020-02-03T20:12:47	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.255
2020-02-11T18:11:21	IanGlencross	glenx24	50000	5000000						3	0.255
2020-02-18T17:47:43	daveward2005	MW	50000	5000000						3	0.255
2020-02-26T01:38:16	IanGlencross	glenx24	50000	5000000						3	0.255
2020-03-10T07:09:20	Bommer	3770K	50000	5000000						3	0.255
2020-03-10T17:07:03	mnd9	75201b	50000	5000000						3	0.255
2020-03-18T02:07:29	mnd9	office2	50000	5000000						3	0.255
2020-03-28T20:55:25	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-04-10T08:36:37	daveward2005	MW	50000	5000000						3	0.255
2020-04-22T14:33:36	mnd9	office2	50000	5000000						3	0.255
2020-04-30T05:40:05	nordi	sweet16	50000	5000000						3	0.255
2020-05-11T08:02:21	nordi	sweet16	50000	5000000						3	0.255
2020-05-26T12:12:11	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-06-13T21:26:12	mnd9	kitchen	50000	5000000						3	0.255
2020-06-28T04:47:18	IanGlencross	glenx24	50000	5000000						3	0.255
2020-07-05T03:29:40	lycorn	colab_S	50000	5000000						3	0.255
2020-07-11T20:34:58	GAN	PG-HP	50000	5000000	12012615541526451980584831	83.313	2	2	4616180254748498	2	0.170

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	Ethan O'Connor	v4_computers	3F0F1E6C799D7573	0.135
2016-07-15T23:04:07	Mark Rose	raphael	3F0F1E6C799D7573	0.135

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 135000, B2 = 2868750 (P-1 stage 2)

B1 = 166298 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 280000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

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

B1 = 4000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

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10³

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10¹⁵

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