M2086543 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	28.5663	69.1176%	2500000	125000000	0.8746	7.8933%	29.4410	71.5553%	2.4376%
PrimeNet	2⁵⁸	0.0184	63.7931%	9000	160000	0.0016	2.6745%	0.0200	64.7615%	0.9684%
GPU72	2⁶²	0.2944	66.1290%	9000	140000	0.0015	1.3998%	0.2960	66.6032%	0.4741%
Difference	+6	+28.2719	+2.9886%	+2491000	+124860000	+0.8731	+6.4935%	+29.1450	+4.9521%	+4.9521%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2086543	40632155142792201268506169	26	85.071	9736716459424081188 2² × 3 × 811393038285340099	2020-07-28	4	811393038285340099	5,745,224	4.215e+9	7.872e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.223%
2009-07-26T17:33:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.876%
2010-12-28T02:16:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.351%
2011-01-08T14:34:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.509%
2011-01-25T08:12:00	James Heinrich	Q6600	135000	2936250		-		-	-	0.027	-	-	2.730%
2016-07-07T00:37:29	Jocelyn Larouche	Manual testing	182337	5872500	12	-		-	-	0.047	-	-	3.348%
2016-11-05T01:34:06	Jocelyn Larouche	low 4M	218804	218804		-		-	-	0.021	-	-	1.225%
2016-11-07T03:11:26	Jocelyn Larouche	low 4M	262564	262564		-		-	-	0.025	-	-	1.342%
2017-04-17T10:02:03	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.893%
2017-05-13T16:00:15	Jocelyn Larouche	low 4M	364674	3646740	6	-		-	-	0.052	-	-	3.331%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T12:49:00	Sturle Sunde	klughardt.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-19T07:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.147	-	-
2013-09-03T09:36:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.470	-	-
2015-04-05T09:11:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.941	-	-
2015-04-05T09:11:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.791	-	-
2015-11-06T09:16:12	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.581	-	-
2016-09-18T04:00:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.163	-	-
2019-04-01T03:15:23	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.33	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.608 GHz-days
Estimated T-Level:	22.018

Digits	B1	Curves	Complete	FacMiss
20	11000	113 / 100	1.130	32.120%
25	50000	113 / 280	0.404	66.745%

New Calculation Method

Total ECM effort:	9.608 GHz-days
Estimated T-Level:	22.018

Digits	B1	Complete	FacMiss
20	11000	3.645	2.612%
25	50000	0.329	71.932%
30	250000	0.020	97.992%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		111	9.438
50000	5000000	40632155142792201268506169	2	0.170

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-05T18:30:00	S36049	Wolle3	50000	5000000						3	0.255
2009-11-03T21:59:00	James Hintz	ryan	50000	5000000						3	0.255
2011-05-23T14:54:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-19T16:31:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-09-05T10:13:00	OS1	L3	50000	5000000						3	0.255
2015-07-26T19:14:00	guru	w6	50000	5000000						3	0.255
2016-02-20T11:26:50	Sintax	cloud2	50000	5000000						3	0.255
2016-05-20T18:52:45	lettp	Home	50000	5000000						3	0.255
2016-07-27T16:31:11	Bruce	test	50000	5000000						3	0.255
2017-01-15T03:17:06	Bruce	Desk6	50000	5000000						3	0.255
2017-08-02T22:14:44	Bruce	Desk6	50000	5000000						3	0.255
2017-12-25T18:07:47	Bruce	Desk6	50000	5000000						3	0.255
2018-05-22T18:14:07	Bruce	Desk6	50000	5000000						3	0.255
2018-10-23T19:52:15	Bruce	Desk6	50000	5000000						3	0.255
2020-01-03T20:26:46	TheJudger	myECM	50000	5000000						3	0.255
2020-01-10T13:15:09	EricP	Cannonfodder	50000	5000000						3	0.255
2020-01-20T09:02:35	mnd9	office2	50000	5000000						3	0.255
2020-01-24T01:42:54	Bommer	2600X	50000	5000000						3	0.255
2020-02-01T01:08:21	daveward2005	Davy	50000	5000000						3	0.255
2020-02-15T07:18:28	S04803	lfmcal	50000	5000000						3	0.255
2020-02-17T08:44:10	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-02-25T01:02:41	cappy95833	HomePC	50000	5000000						3	0.255
2020-03-02T19:55:46	kracker	O0	50000	5000000						3	0.255
2020-03-08T20:06:54	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-03-16T14:33:01	mnd9	25836b	50000	5000000						3	0.255
2020-03-25T19:33:17	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.255
2020-04-06T20:44:13	daveward2005	Davy	50000	5000000						3	0.255
2020-04-20T10:01:07	mnd9	eileen	50000	5000000						3	0.255
2020-04-28T00:55:17	mnd9	l2lounge	50000	5000000						3	0.255
2020-05-08T11:34:26	nordi	sweet16	50000	5000000						3	0.255
2020-05-21T21:11:35	alpertron	laptop3	50000	5000000						3	0.255
2020-06-11T06:39:28	Leo Custodio	GCP-013	50000	5000000						3	0.255
2020-06-25T23:25:42	Nesowa	6700T	50000	5000000						3	0.255
2020-07-03T17:38:01	GAN	OSB-01	50000	5000000						3	0.255
2020-07-10T03:28:53	GAN	LMS-14	50000	5000000						3	0.255
2020-07-15T23:20:24	GAN	LMS-14	50000	5000000						3	0.255
2020-07-22T07:37:42	daveward2005	Dave2	50000	5000000						3	0.255
2020-07-28T22:34:47	daveward2005	Dave2	50000	5000000	40632155142792201268506169	85.071	2	2		2	0.170

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	7E4D4A8BCD29E9DF	0.137

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 = 364674, B2 = 3646740 (P-1 stage 2)

B1 = 182337, B2 = 5872500 (P-1 stage 2)

B1 = 364674 (P-1 stage 1)

B1 = 135000, B2 = 2936250 (P-1 stage 2)

B1 = 262564 (P-1 stage 1)

B1 = 218804 (P-1 stage 1)

B1 = 182337 (P-1 stage 1)

B1 = 135000 (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)

10⁰

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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