M1866547 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	2⁶⁷	15.9192	68.6567%	2149908	77396688	0.4916	7.7754%	16.4108	71.0938%	2.4371%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0281%	0.0116	64.2735%	1.1156%
GPU72	2⁶¹	0.1646	65.5738%	10000	150000	0.0014	1.6890%	0.1660	66.1552%	0.5815%
Difference	+6	+15.7546	+3.0829%	+2139908	+77246688	+0.4902	+6.0864%	+16.2448	+4.9386%	+4.9386%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1866547	7776448780060252439633	22	72.720	2083110894089528 2³ × 577 × 451280522983	2018-02-26	577	451280522983	759.48	1,934.1	3,612.3

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-08T01:00:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.927%
2015-10-07T06:42:30	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	5.081%
2016-09-05T18:28:58	Jocelyn Larouche	low4M	500000	30000000	12	-		-	-	0.166	-	-	5.744%
2016-09-30T05:55:09	Jocelyn Larouche	low 4M	500000	33000000	6	-		-	-	0.179	-	-	5.836%
2016-10-07T05:52:37	Jocelyn Larouche	low 4M	500000	39600000	6	-		-	-	0.207	-	-	6.014%
2016-11-03T20:53:41	Jocelyn Larouche	low 4M	600000	600000		-		-	-	0.047	-	-	2.159%
2016-12-19T18:36:38	Jocelyn Larouche	low 4M	720000	720000		-		-	-	0.057	-	-	2.324%
2016-12-30T23:10:09	Jocelyn Larouche	low 4M	864000	864000		-		-	-	0.068	-	-	2.496%
2017-01-14T05:24:38	Jocelyn Larouche	low 4M	1036800	1036800		-		-	-	0.082	-	-	2.675%
2017-02-19T20:41:22	Jocelyn Larouche	low 4M	1244160	12441600	12	-		-	-	0.146	-	-	5.354%
2017-03-25T20:16:12	Jocelyn Larouche	low 4M	1492992	14929920	12	-		-	-	0.175	-	-	5.634%
2017-05-22T21:10:27	Jocelyn Larouche	low 4M	1791590	17915900	12	-		-	-	0.210	-	-	5.920%
2017-06-14T03:17:00	Jocelyn Larouche	low 4M	2149908	38698344	12	-		-	-	0.326	-	-	6.927%
2018-02-17T12:12:00	Jocelyn Larouche	low 4M	2149908	77396688	12	-		-	-	0.492	-	-	7.775%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:56	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.062	-	-
2010-04-06T23:36:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.082	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.165	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.855	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.526	-	-
2015-05-07T23:39:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.052	-	-
2015-05-07T23:39:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.002	-	-
2015-09-10T08:47:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.004	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.153 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.153 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.544	0.019%
25	50000	0.774	46.121%
30	250000	0.048	95.327%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		48	3.323
50000	5000000	7776448780060252439633	2	0.138
50000	6600000		201	15.69

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-30T17:27:00	Scott Kurowski	UW1	50000	5000000						3	0.208
2009-07-21T10:01:00	James Hintz	08_071509	50000	5000000						3	0.208
2011-03-13T04:17:00	Lupo	yorick	50000	5000000						3	0.208
2012-09-01T20:13:00	abhi	abhi-PC	50000	5000000						3	0.208
2013-10-02T08:18:00	OS1	L3	50000	5000000						3	0.208
2014-06-14T08:46:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-03-22T13:43:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-11-14T20:52:28	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2016-02-28T05:07:47	Bruce	DESK3	50000	5000000						3	0.208
2016-04-10T16:37:25	Bruce	DESK3	50000	5000000						3	0.208
2016-06-18T07:16:57	Bruce	DESK3	50000	5000000						3	0.208
2016-09-23T11:37:37	Bruce	DESK3	50000	5000000						3	0.208
2017-05-31T14:40:49	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-06-17T22:33:04	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-09-07T12:28:19	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-12-30T02:40:28	Bruce	DESK3	50000	5000000						3	0.208
2018-02-26T16:25:02	Bruce	DESK3	50000	5000000	7776448780060252439633	72.720	2	2		2	0.138
2021-08-13T08:30:38	TJAOI	Manual testing	50000	6600000						201	15.69

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	9F050E291E227F36	0.101
2015-06-28T05:06:00	MadPoo	Manual testing	9F050E291E227F36	0.101

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 = 2149908, B2 = 77396688 (P-1 stage 2)

B1 = 2149908, B2 = 38698344 (P-1 stage 2)

B1 = 1791590, B2 = 17915900 (P-1 stage 2)

B1 = 500000, B2 = 39600000 (P-1 stage 2)

B1 = 500000, B2 = 33000000 (P-1 stage 2)

B1 = 1492992, B2 = 14929920 (P-1 stage 2)

B1 = 2149908 (P-1 stage 1)

B1 = 500000, B2 = 30000000 (P-1 stage 2)

B1 = 1244160, B2 = 12441600 (P-1 stage 2)

B1 = 1791590 (P-1 stage 1)

B1 = 1492992 (P-1 stage 1)

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

B1 = 1244160 (P-1 stage 1)

B1 = 1036800 (P-1 stage 1)

B1 = 864000 (P-1 stage 1)

B1 = 720000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (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