M1887451 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	31.5796	69.1176%	3095866	188745100	1.0392	8.4521%	32.6187	71.7278%	2.6102%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0343%	0.0115	64.2758%	1.1179%
GPU72	2⁶¹	0.1627	65.5738%	10000	150000	0.0014	1.6928%	0.1641	66.1565%	0.5828%
Difference	+7	+31.4168	+3.5439%	+3085866	+188595100	+1.0378	+6.7593%	+32.4546	+5.5713%	+5.5713%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1887451	2335848842350960400997079	25	80.950	618783969054285489 3 × 7 × 13 × 49711 × 45595702063	2020-07-22	49711	45595702063	146,835	195.42	364.97

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-18T01:00:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.541%
2015-10-07T20:51:34	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	4.617%
2016-09-22T11:43:16	Jocelyn Larouche	low 4M	500000	16500000	12	-		-	-	0.108	-	-	4.701%
2016-10-07T05:52:33	Jocelyn Larouche	low 4M	500000	19800000	6	-		-	-	0.122	-	-	4.861%
2016-10-10T15:05:07	Jocelyn Larouche	low 4M	500000	50000000	12	-		-	-	0.251	-	-	5.692%
2016-11-03T20:53:43	Jocelyn Larouche	low 4M	600000	600000		-		-	-	0.047	-	-	1.927%
2016-12-24T02:11:48	Jocelyn Larouche	low 4M	720000	720000		-		-	-	0.057	-	-	2.079%
2016-12-29T21:51:13	Jocelyn Larouche	low 4M	864000	864000		-		-	-	0.068	-	-	2.238%
2017-01-21T06:59:37	Jocelyn Larouche	low 4M	1036800	1036800		-		-	-	0.082	-	-	2.403%
2017-03-01T23:52:31	Jocelyn Larouche	low 4M	1244160	12441600	12	-		-	-	0.146	-	-	4.887%
2017-06-19T04:39:21	Jocelyn Larouche	low 4M	1492992	26873856	12	-		-	-	0.226	-	-	5.778%
2017-07-18T02:33:41	Jocelyn Larouche	low 4M	1791590	17915900	12	-		-	-	0.210	-	-	5.419%
2017-07-30T02:46:00	Jocelyn Larouche	low 4M	2149908	21499080	12	-		-	-	0.252	-	-	5.694%
2017-08-04T01:13:06	Jocelyn Larouche	low 4M	2579889	25798890	12	-		-	-	0.302	-	-	5.976%
2017-08-11T00:31:28	Jocelyn Larouche	low 4M	3095866	30958660	12	-		-	-	0.363	-	-	6.263%
2018-02-16T12:53:16	Jocelyn Larouche	low 4M	3095866	61917320	12	-		-	-	0.496	-	-	7.099%
2018-03-14T11:52:42	Jocelyn Larouche	low 4M	3095866	123834640	12	-		-	-	0.761	-	-	7.939%
2018-05-02T11:49:43	Jocelyn Larouche	low 4M	3095866	188745100	12	-		-	-	1.039	-	-	8.452%

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		-	-	0.020	-	-
2016-02-23T16:28:56	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.061	-	-
2010-04-02T14:24:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.081	-	-
2016-02-23T16:28:57	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.163	-	-
2011-03-08T05:15:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.846	-	-
2016-02-23T16:28:56	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.520	-	-
2015-05-10T08:11:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.040	-	-
2015-05-10T08:11:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	1.980	-	-
2015-09-13T19:11:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.959	-	-
2018-05-07T13:42:44	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	7.918	-	-
2019-06-17T12:14:56	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	15.84	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.373 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:	18.373 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.341	0.024%
25	50000	0.755	47.009%
30	250000	0.047	95.447%
35	1000000	0.002	99.786%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		138	9.57
50000	5000000	2335848842350960400997079	3	0.208
50000	6600000		110	8.600

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-01T04:12:00	James Heinrich	Q6600	50000	5000000						3	0.208
2009-07-24T21:27:00	SubPrime	mysql0	50000	5000000						3	0.208
2011-03-24T01:56:00	Lupo	yorick	50000	5000000						3	0.208
2012-09-27T22:35:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.208
2013-10-14T09:59:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2014-07-08T10:23:00	Sara	Sara	50000	5000000						3	0.208
2015-04-12T14:30:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-12-07T22:56:49	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2016-03-03T19:29:33	Bruce	DESK3	50000	5000000						3	0.208
2016-04-18T05:29:16	Bruce	DESK3	50000	5000000						3	0.208
2016-07-22T13:28:02	Bruce	DESK3	50000	5000000						3	0.208
2016-10-02T13:06:24	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2016-12-05T16:01:34	Bruce	DESK3	50000	5000000						3	0.208
2017-02-24T09:40:14	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-09-26T00:50:47	ANONYMOUS	Worker	50000	5000000						3	0.208
2018-01-11T06:24:29	Bruce	DESK3	50000	5000000						3	0.208
2019-10-08T10:14:54	ANONYMOUS	TimeVampireTheFifth	50000	5000000						3	0.208
2019-12-01T13:46:52	penlu	grizzly	50000	5000000						3	0.208
2019-12-04T16:51:36	J.R. Allen	lapdell	50000	5000000						3	0.208
2019-12-08T23:52:34	J.R. Allen	lapacer	50000	5000000						3	0.208
2019-12-18T15:25:20	S04803	lfmcal	50000	5000000						3	0.208
2019-12-19T06:06:10	Nesowa	entropy_generator_2	50000	5000000						3	0.208
2019-12-24T08:16:10	George Woltman	colab	50000	5000000						3	0.208
2019-12-29T23:41:02	TheJudger	myECM	50000	5000000						3	0.208
2020-01-03T20:04:36	TheJudger	myECM	50000	5000000						3	0.208
2020-01-10T16:57:51	daveward2005	MW	50000	5000000						3	0.208
2020-01-18T14:38:03	mnd9	221Rb	50000	5000000						3	0.208
2020-02-01T10:45:10	daveward2005	MW	50000	5000000						3	0.208
2020-02-10T08:06:36	Alvin Bunk	BADCAT	50000	5000000						3	0.208
2020-02-17T14:00:46	mnd9	75201b	50000	5000000						3	0.208
2020-02-24T23:27:24	Nesowa	6700T	50000	5000000						3	0.208
2020-03-02T13:46:35	MarkS	laptop64	50000	5000000						3	0.208
2020-03-08T16:31:52	daveward2005	MW	50000	5000000						3	0.208
2020-03-16T02:14:40	mnd9	l2lounge	50000	5000000						3	0.208
2020-03-24T06:46:13	Keysarecool	HPLaptop	50000	5000000						3	0.208
2020-03-26T12:49:43	Sebastian Hornbostel	NZXT	50000	5000000						3	0.208
2020-04-07T05:58:09	daveward2005	MW	50000	5000000						3	0.208
2020-04-20T15:14:33	nordi	sweet16	50000	5000000						3	0.208
2020-04-28T00:35:36	mnd9	l2lounge	50000	5000000						3	0.208
2020-05-08T06:40:43	nordi	sweet16	50000	5000000						3	0.208
2020-05-22T03:03:10	mnd9	kitchen	50000	5000000						3	0.208
2020-06-09T07:13:03	lycorn	colab_S	50000	5000000						3	0.208
2020-06-25T08:49:48	GAN	PG-HP	50000	5000000						3	0.208
2020-07-03T14:53:15	GAN	OSB-02	50000	5000000						3	0.208
2020-07-10T14:51:31	mnd9	libproj	50000	5000000						3	0.208
2020-07-15T22:42:26	GAN	LMS-08	50000	5000000						3	0.208
2020-07-22T07:37:45	daveward2005	Dave2	50000	5000000	2335848842350960400997079	80.950	3	2		3	0.208
2021-10-28T13:39:55	TJAOI	Manual testing	50000	6600000						110	8.600

date	userid	compid	res64	spent (GHz-days)
1999-09-22T00:00:00	ANONYMOUS	v4_computers	6C06A90A70EEEC31	0.102
2015-07-06T20:15:00	MadPoo	Manual testing	6C06A90A70EEEC31	0.102

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 = 3095866, B2 = 188745100 (P-1 stage 2)

B1 = 3095866, B2 = 123834640 (P-1 stage 2)

B1 = 3095866, B2 = 61917320 (P-1 stage 2)

B1 = 3095866, B2 = 30958660 (P-1 stage 2)

B1 = 2579889, B2 = 25798890 (P-1 stage 2)

B1 = 2149908, B2 = 21499080 (P-1 stage 2)

B1 = 500000, B2 = 50000000 (P-1 stage 2)

B1 = 3095866 (P-1 stage 1)

B1 = 1492992, B2 = 26873856 (P-1 stage 2)

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

B1 = 2579889 (P-1 stage 1)

B1 = 2149908 (P-1 stage 1)

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

B1 = 1791590 (P-1 stage 1)

B1 = 500000, B2 = 19800000 (P-1 stage 2)

B1 = 1492992 (P-1 stage 1)

B1 = 500000, B2 = 16500000 (P-1 stage 2)

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)

10³

10⁴

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10⁶

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10³

10⁴

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10¹⁰

10¹¹

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