M2093123 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	28.4765	69.1176%	2500000	125000000	0.8746	7.8957%	29.3512	71.5560%	2.4384%
PrimeNet	2⁵⁸	0.0183	63.7931%	9000	160000	0.0016	2.6761%	0.0200	64.7620%	0.9689%
GPU72	2⁶²	0.2935	66.1290%	9000	140000	0.0015	1.4007%	0.2951	66.6035%	0.4744%
Difference	+6	+28.1830	+2.9886%	+2491000	+124860000	+0.8731	+6.4950%	+29.0561	+4.9526%	+4.9526%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2093123	2720729952583458350043241560391	31	101.102	649921182984339274386465 3 × 5 × 43328078865622618292431	2020-07-24	5	43328078865622618292431	8.951e+10	2.251e+14	4.203e+14

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.223%
2009-07-27T03:06:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.876%
2010-12-28T23:08:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.351%
2011-01-09T14:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.510%
2011-01-19T10:33:00	James Heinrich	Q6600	140000	3150000		-		-	-	0.029	-	-	2.793%
2016-07-27T10:56:33	Jocelyn Larouche	Manual testing	186340	6300000	12	-		-	-	0.050	-	-	3.411%
2016-11-05T16:28:43	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.239%
2016-11-10T03:36:29	Jocelyn Larouche	low 4M	268329	268329		-		-	-	0.026	-	-	1.358%
2017-05-15T00:37:23	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.896%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	Ethan O'Connor	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T12:44:00	Sturle Sunde	kraus.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-23T17:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.147	-	-
2013-09-03T09:36:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.469	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.938	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.785	-	-
2015-11-06T09:16:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.570	-	-
2016-09-22T02:15:57	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.140	-	-
2019-04-01T03:15:25	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.28	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.272 GHz-days
Estimated T-Level:	21.946

Digits	B1	Curves	Complete	FacMiss
20	11000	109 / 100	1.090	33.438%
25	50000	109 / 280	0.389	67.707%

New Calculation Method

Total ECM effort:	9.272 GHz-days
Estimated T-Level:	21.946

Digits	B1	Complete	FacMiss
20	11000	3.516	2.971%
25	50000	0.318	72.776%
30	250000	0.020	98.062%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		108	9.187
50000	5000000	2720729952583458350043241560391	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-06T02:23:00	oodaira	Win02	50000	5000000						3	0.255
2009-11-08T11:50:00	ANONYMOUS	fn-asterisk	50000	5000000						3	0.255
2011-06-07T01:54:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-25T22:35:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-09-24T17:42:00	arnaud	srv-630	50000	5000000						3	0.255
2015-07-28T21:56:00	guru	w6	50000	5000000						3	0.255
2016-02-20T16:06:40	Sintax	cloud2	50000	5000000						3	0.255
2016-05-23T19:45:10	Bruce	Desk6	50000	5000000						3	0.255
2016-08-11T13:24:11	Bruce	test	50000	5000000						3	0.255
2017-01-21T11:08:12	Bruce	Desk6	50000	5000000						3	0.255
2017-08-10T07:49:36	Bruce	Desk6	50000	5000000						3	0.255
2017-12-29T15:07:27	Bruce	Desk6	50000	5000000						3	0.255
2018-05-31T07:32:36	Bruce	Desk6	50000	5000000						3	0.255
2019-02-19T04:28:52	zar	eng1	50000	5000000						3	0.255
2020-01-05T19:07:22	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-01-13T07:35:02	daveward2005	Davy	50000	5000000						3	0.255
2020-01-23T06:05:37	DRMEDESY	hm02	50000	5000000						3	0.255
2020-01-26T13:04:27	mnd9	25836b	50000	5000000						3	0.255
2020-02-04T01:40:27	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-02-12T12:50:47	David_McCann	i5	50000	5000000						3	0.255
2020-02-19T04:12:52	mnd9	office2	50000	5000000						3	0.255
2020-02-26T18:35:47	cappy95833	HomePC	50000	5000000						3	0.255
2020-03-04T21:04:34	mnd9	colab	50000	5000000						3	0.255
2020-03-10T17:55:09	mnd9	office2	50000	5000000						3	0.255
2020-03-18T06:22:30	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-03-29T14:35:44	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-04-10T18:39:48	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.255
2020-04-23T00:35:55	nordi	sweet16	50000	5000000						3	0.255
2020-04-30T05:16:55	mnd9	221Rb	50000	5000000						3	0.255
2020-05-12T03:45:18	mnd9	75203b	50000	5000000						3	0.255
2020-05-26T12:09:56	mnd9	kitchen	50000	5000000						3	0.255
2020-06-14T12:57:05	alpertron	laptop3	50000	5000000						3	0.255
2020-06-28T12:15:11	GAN	GAN-HP	50000	5000000						3	0.255
2020-07-05T09:25:31	GAN	LMS-03	50000	5000000						3	0.255
2020-07-12T00:19:50	GAN	LMS-03	50000	5000000						3	0.255
2020-07-18T22:47:09	mnd9	25836b	50000	5000000						3	0.255
2020-07-24T01:15:53	GAN	LMS-17	50000	5000000	2720729952583458350043241560391	101.102	1	2	5977222892767472	1	0.085

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	ANONYMOUS	v4_computers	AAC8AC23F3C352BD	0.138
2017-06-12T12:29:14	kkmrkkblmbrbk	c4.large	AAC8AC23F3C352BD	0.138

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 = 186340, B2 = 6300000 (P-1 stage 2)

B1 = 140000, B2 = 3150000 (P-1 stage 2)

B1 = 268329 (P-1 stage 1)

B1 = 223608 (P-1 stage 1)

B1 = 186340 (P-1 stage 1)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (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 = 2048 (P-1 stage 1)

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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