M1827901 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	32.6084	69.1176%	2384605	182790100	0.9608	8.2045%	33.5691	71.6514%	2.5337%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8785%	0.0117	64.2184%	1.0605%
GPU72	2⁶¹	0.1681	65.5738%	9000	140000	0.0013	1.5942%	0.1693	66.1226%	0.5488%
Difference	+7	+32.4403	+3.5439%	+2375605	+182650100	+0.9595	+6.6102%	+33.3998	+5.5288%	+5.5288%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1827901	1433543234394192005599	22	70.280	392128248300699 3 × 4523 × 28898831771	2021-02-12	4523	28898831771	252.46	123.85	231.32

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-12-31T16:01:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.526%
2015-10-06T21:30:12	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	4.599%
2016-08-23T15:10:32	Jocelyn Larouche	Manual testing	500000	30000000	12	-		-	-	0.166	-	-	5.211%
2016-10-07T05:52:36	Jocelyn Larouche	low 4M	500000	36000000	6	-		-	-	0.191	-	-	5.374%
2016-10-27T15:20:23	Jocelyn Larouche	low 4M	798600	798600		-		-	-	0.063	-	-	2.159%
2016-10-29T20:53:42	Jocelyn Larouche	low 4M	958320	958320		-		-	-	0.075	-	-	2.321%
2017-03-21T00:47:12	Jocelyn Larouche	low 4M	1379980	13799800	12	-		-	-	0.162	-	-	5.017%
2017-03-29T03:10:18	Jocelyn Larouche	low 4M	1655976	16559760	12	-		-	-	0.194	-	-	5.283%
2017-03-31T06:29:11	Jocelyn Larouche	low 4M	1987171	19871710	12	-		-	-	0.233	-	-	5.555%
2017-05-22T21:10:26	Jocelyn Larouche	low 4M	2384605	23846050	12	-		-	-	0.280	-	-	5.833%
2018-02-08T17:39:28	Jocelyn Larouche	low 4M	2384605	47692100	12	-		-	-	0.382	-	-	6.634%
2018-02-24T11:25:43	Jocelyn Larouche	low 4M	2384605	95384200	12	-		-	-	0.586	-	-	7.441%
2018-09-12T18:46:13	Jocelyn Larouche	low 4M	2384605	182790100	12	-		-	-	0.961	-	-	8.204%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-09T22:34:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.168	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.873	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.537	-	-
2015-04-25T21:24:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.074	-	-
2015-04-25T21:24:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.044	-	-
2015-09-04T17:59:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.088	-	-
2018-04-23T13:17:24	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.176	-	-
2019-06-24T09:36:03	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.35	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.861 GHz-days
Estimated T-Level:	24.714

Digits	B1	Curves	Complete	FacMiss
20	11000	264 / 100	2.640	7.042%
25	50000	264 / 280	0.943	38.886%

New Calculation Method

Total ECM effort:	18.861 GHz-days
Estimated T-Level:	24.714

Digits	B1	Complete	FacMiss
20	11000	8.677	0.017%
25	50000	0.785	45.615%
30	250000	0.048	95.273%
35	1000000	0.002	99.778%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		187	12.91
50000	5000000	1433543234394192005599	6	0.414
50000	6600000		70	5.450
60000	6000000		1	0.083

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-19T23:55:00	Scott Kurowski	D-3000	50000	5000000						3	0.207
2009-07-17T14:16:00	James Hintz	15_071509	50000	5000000						3	0.207
2011-01-06T16:18:00	c10ck3r	aleman	50000	5000000						3	0.207
2012-05-26T15:47:00	omiXorp	LLB16-T5500-21	50000	5000000						3	0.207
2013-08-13T01:00:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-01T13:11:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-10-12T20:05:00	mikr	MSI	50000	5000000						12	0.829
2016-05-28T05:22:39	Bruce	DESK3	50000	5000000						3	0.207
2016-09-01T01:12:37	Bruce	DESK3	50000	5000000						3	0.207
2016-11-10T20:30:14	Bruce	DESK3	50000	5000000						3	0.207
2017-01-09T06:31:41	Bruce	DESK3	50000	5000000						3	0.207
2017-04-29T16:02:10	ANONYMOUS	Worker	50000	5000000						3	0.207
2017-12-02T02:45:46	Bruce	DESK3	50000	5000000						3	0.207
2018-02-05T15:54:37	Bruce	DESK3	50000	5000000						3	0.207
2019-11-22T01:37:22	Dylan Delgado	colab	50000	5000000						3	0.207
2019-11-24T19:47:08	J.R. Allen	lapdell	50000	5000000						3	0.207
2019-11-26T09:00:32	chuenkit	CHAIN	50000	5000000						3	0.207
2019-11-30T04:41:51	Malott	pm09	50000	5000000						3	0.207
2019-12-03T20:10:43	J.R. Allen	lapacer	50000	5000000						3	0.207
2019-12-08T02:04:41	Alvin Bunk	BADCAT	50000	5000000						3	0.207
2019-12-12T11:31:36	daveward2005	Davy	50000	5000000						3	0.207
2019-12-18T16:37:29	mnd9	75211backdoorb	50000	5000000						3	0.207
2019-12-23T06:12:13	Nesowa	6700T	50000	5000000						3	0.207
2020-01-02T23:14:47	Keysarecool	Boat_Anchor	50000	5000000						3	0.207
2020-01-09T02:28:30	daveward2005	Davy	50000	5000000						3	0.207
2020-01-12T14:19:25	mnd9	office2	50000	5000000						3	0.207
2020-01-17T15:55:04	IEFBR14	MK1	50000	5000000						3	0.207
2020-01-23T06:53:19	David_McCann	i5	50000	5000000						3	0.207
2020-01-30T02:21:49	David_McCann	i5	50000	5000000						3	0.207
2020-02-08T11:57:52	David_McCann	i5	50000	5000000						3	0.207
2020-02-16T05:31:23	mnd9	libproj	50000	5000000						3	0.207
2020-02-23T16:12:31	Brett Walker	brain	50000	5000000						3	0.207
2020-03-01T01:17:42	IanGlencross	glenx24	50000	5000000						3	0.207
2020-03-07T07:11:14	mnd9	75201b	50000	5000000						3	0.207
2020-03-14T14:06:50	mnd9	office2	50000	5000000						3	0.207
2020-04-03T18:13:45	EricP	Cannonfodder	50000	5000000						3	0.207
2020-04-18T00:44:31	Keysarecool	Boat_Anchor	50000	5000000						3	0.207
2020-04-26T13:00:29	mnd9	fb	50000	5000000						3	0.207
2020-05-05T04:48:27	mnd9	eileen	50000	5000000						3	0.207
2020-05-17T13:49:56	mnd9	libproj	50000	5000000						3	0.207
2020-05-19T22:21:26	mnd9	kitchen	50000	5000000						3	0.207
2020-06-04T20:32:31	nordi	sweet16	50000	5000000						3	0.207
2020-06-26T15:18:40	GAN	KL-SCH01	50000	5000000						3	0.207
2020-07-02T04:57:10	debrouxl	8rd	50000	5000000						3	0.207
2020-07-08T17:44:16	GAN	LMS-16	50000	5000000						3	0.207
2020-07-14T17:37:25	GAN	LMS-15	50000	5000000						3	0.207
2020-07-20T22:29:37	GAN	LMS-12	50000	5000000						3	0.207
2020-07-27T07:40:31	GAN	LMS-15	50000	5000000						3	0.207
2020-08-03T17:15:58	GAN	OSB-02	50000	5000000						3	0.207
2020-08-11T14:02:47	GAN	LMS-03	50000	5000000						3	0.207
2020-08-28T14:32:35	MarkS	desktop-i7	50000	5000000						7	0.483
2020-10-02T05:08:36	GAN	KA-HP	50000	5000000						7	0.483
2020-10-28T17:11:13	rextherunt	ice	50000	5000000						7	0.483
2020-12-02T11:07:18	Peredron	Peredron2	60000	6000000						1	0.083
2021-01-15T18:53:37	Chang Chia-Tche	ex-ctcpc	50000	5000000						7	0.483
2021-02-12T09:32:28	mnd9	f4	50000	5000000	1433543234394192005599	70.280	6	2	5166182012289057	6	0.414
2021-04-16T16:25:05	TJAOI	Manual testing	50000	6600000						70	5.450

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	ANONYMOUS	v4_computers	DA1B0E9727E912__	0.099
1999-03-15T00:00:00	Dry Creek Photo	v4_computers	6E0FCC07ED74A730	0.099
2015-06-27T00:56:00	MadPoo	Manual testing	6E0FCC07ED74A730	0.099

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 = 2384605, B2 = 182790100 (P-1 stage 2)

B1 = 2384605, B2 = 95384200 (P-1 stage 2)

B1 = 2384605, B2 = 47692100 (P-1 stage 2)

B1 = 2384605, B2 = 23846050 (P-1 stage 2)

B1 = 1987171, B2 = 19871710 (P-1 stage 2)

B1 = 1655976, B2 = 16559760 (P-1 stage 2)

B1 = 500000, B2 = 36000000 (P-1 stage 2)

B1 = 2384605 (P-1 stage 1)

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

B1 = 1379980, B2 = 13799800 (P-1 stage 2)

B1 = 1987171 (P-1 stage 1)

B1 = 1655976 (P-1 stage 1)

B1 = 1379980 (P-1 stage 1)

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

B1 = 958320 (P-1 stage 1)

B1 = 798600 (P-1 stage 1)

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

B1 = 500000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

10²

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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