M1849457 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	32.2283	69.1176%	1849457	184945700	0.9302	8.0378%	33.1585	71.5999%	2.4822%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0229%	0.0117	64.2716%	1.1137%
GPU72	2⁶¹	0.1661	65.5738%	9000	150000	0.0013	1.6309%	0.1674	66.1352%	0.5614%
Difference	+7	+32.0622	+3.5439%	+1840457	+184795700	+0.9289	+6.4069%	+32.9911	+5.4647%	+5.4647%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1849457	375150046600695976050721481	27	88.278	101421673118297958820 2² × 5 × 641 × 60041 × 131763410861	2020-12-08	60041	131763410861	46,953,019	564.71	1,054.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-02T21:45:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.532%
2015-10-06T23:39:08	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	4.605%
2016-10-29T20:53:43	Jocelyn Larouche	low 4M	864000	864000		-		-	-	0.068	-	-	2.232%
2016-12-18T19:36:11	Jocelyn Larouche	low 4M	720000	720000		-		-	-	0.057	-	-	2.073%
2017-01-12T03:16:24	Jocelyn Larouche	low 4M	1036800	1036800		-		-	-	0.082	-	-	2.396%
2017-02-11T17:53:08	Jocelyn Larouche	low 4M	1244160	12441600	12	-		-	-	0.146	-	-	4.876%
2018-01-31T13:05:35	Jocelyn Larouche	low 4M	1849457	24883200	12	-		-	-	0.244	-	-	5.782%
2018-02-09T20:02:42	Jocelyn Larouche	low 4M	1849457	49766400	12	-		-	-	0.351	-	-	6.554%
2018-02-24T22:02:46	Jocelyn Larouche	low 4M	1849457	99532800	12	-		-	-	0.564	-	-	7.334%
2018-09-24T11:55:46	Jocelyn Larouche	low 4M	1849457	184945700	12	-		-	-	0.930	-	-	8.038%

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	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.062	-	-
2010-04-09T00:10:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.083	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.166	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.863	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.531	-	-
2015-04-28T21:21:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.062	-	-
2015-04-28T21:21:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.020	-	-
2015-09-08T08:29:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.041	-	-
2017-09-01T10:33:56	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.081	-	-
2019-06-17T12:14:58	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.16	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.966 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:	17.966 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.250	0.026%
25	50000	0.746	47.415%
30	250000	0.046	95.502%
35	1000000	0.002	99.789%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		177	12.24
50000	5000000	375150046600695976050721481	5	0.346
50000	6600000		69	5.380

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-23T11:02:00	Scott Kurowski	HomeOffice	50000	5000000						3	0.207
2009-07-22T15:31:00	Lukasz Wrobel	cm-3	50000	5000000						3	0.207
2011-01-26T17:50:00	James Hintz	ryan	50000	5000000						3	0.207
2012-07-11T16:41:00	Lukasz Wrobel	i-1	50000	5000000						3	0.207
2013-09-14T00:05:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-30T10:53:00	Sara	Sara	50000	5000000						3	0.207
2014-12-21T00:48:00	mikr	MSI	50000	5000000						12	0.830
2016-06-06T20:35:19	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-09-12T14:14:24	Bruce	DESK3	50000	5000000						3	0.207
2016-11-20T19:10:34	Bruce	DESK3	50000	5000000						3	0.207
2017-01-24T10:37:51	deo2016	3CPU	50000	5000000						3	0.207
2017-07-15T03:36:34	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-12-19T13:51:35	Bruce	DESK3	50000	5000000						3	0.207
2018-02-17T08:42:22	Bruce	DESK3	50000	5000000						3	0.207
2019-11-27T05:02:29	IanGlencross	glenx24	50000	5000000						3	0.207
2019-11-27T21:09:31	MarkS	laptop64	50000	5000000						3	0.207
2019-12-02T02:54:47	penlu	grizzly	50000	5000000						3	0.207
2019-12-05T02:55:30	Nesowa	entropy_generator_2	50000	5000000						3	0.207
2019-12-09T01:13:46	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.207
2019-12-13T10:17:10	mnd9	75211cornerb	50000	5000000						3	0.207
2019-12-18T10:05:00	mnd9	f3	50000	5000000						3	0.207
2019-12-24T13:50:34	J.R. Allen	lapdell	50000	5000000						3	0.207
2019-12-30T07:27:26	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2020-01-03T19:51:22	IanGlencross	glenx24	50000	5000000						3	0.207
2020-01-11T08:55:04	mnd9	27016	50000	5000000						3	0.207
2020-01-18T18:29:33	IEFBR14	MK1	50000	5000000						3	0.207
2020-01-24T04:24:22	mnd9	75201b	50000	5000000						3	0.207
2020-01-31T15:01:05	IanGlencross	glenx24	50000	5000000						3	0.207
2020-02-10T04:57:53	mnd9	kitchen	50000	5000000						3	0.207
2020-02-17T03:44:45	mnd9	colab	50000	5000000						3	0.207
2020-02-24T14:40:36	mnd9	kitchen	50000	5000000						3	0.207
2020-03-02T12:32:13	mnd9	75211backdoorb	50000	5000000						3	0.207
2020-03-09T05:55:40	Claude Portenier	Petit-Idiot	50000	5000000						3	0.207
2020-03-15T21:20:01	IanGlencross	glenx24	50000	5000000						3	0.207
2020-03-25T13:19:12	kracker	O0	50000	5000000						3	0.207
2020-04-06T08:46:14	Keysarecool	HPLaptop	50000	5000000						3	0.207
2020-04-20T07:59:01	nordi	sweet16	50000	5000000						3	0.207
2020-04-27T23:51:43	daveward2005	Davy	50000	5000000						3	0.207
2020-05-08T12:14:33	IanGlencross	glenx24	50000	5000000						3	0.207
2020-05-21T08:09:00	volki	home	50000	5000000						3	0.207
2020-06-10T04:41:06	Yxinity	Olga	50000	5000000						3	0.207
2020-06-24T20:19:45	Dylan Delgado	colab	50000	5000000						3	0.207
2020-07-03T09:57:00	GAN	LMS-15	50000	5000000						3	0.207
2020-07-10T07:17:21	Ahmed Azhad	colab	50000	5000000						3	0.207
2020-07-15T22:08:43	daveward2005	Dave2	50000	5000000						3	0.207
2020-07-22T02:08:48	GAN	LMS-13	50000	5000000						3	0.207
2020-07-28T17:45:51	daveward2005	Dave2	50000	5000000						3	0.207
2020-08-05T15:11:54	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.207
2020-08-13T21:41:13	Nesowa	6700T	50000	5000000						3	0.207
2020-09-02T09:58:51	M. R. Mayer	nimbus	50000	5000000						7	0.484
2020-10-05T13:27:07	tottenhoff	4-of-4-Ryzen-5-3600	50000	5000000						7	0.484
2020-11-01T15:00:59	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.484
2020-12-08T11:27:58	mnd9	libproj	50000	5000000	375150046600695976050721481	88.278	5	2	1182938799059869	5	0.346
2021-06-18T16:47:58	TJAOI	Manual testing	50000	6600000						69	5.380

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	2A682B1254FA2380	0.100
2015-06-27T00:55:00	MadPoo	Manual testing	2A682B1254FA2380	0.100

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 = 1849457, B2 = 184945700 (P-1 stage 2)

B1 = 1849457, B2 = 99532800 (P-1 stage 2)

B1 = 1849457, B2 = 49766400 (P-1 stage 2)

B1 = 1849457, B2 = 24883200 (P-1 stage 2)

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

B1 = 1849457 (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 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

10³

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10¹⁰

10¹¹

10¹²

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