M1861649 Mersenne number exponent details

is 2 ^1861649 - 1

has 560413 decimal digits

takes 0.101 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	32.0172	69.1176%	2488320	248832000	1.2515	8.6154%	33.2688	71.7783%	2.6606%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0266%	0.0117	64.2730%	1.1151%
GPU72	2⁶¹	0.1650	65.5738%	9000	150000	0.0013	1.6330%	0.1663	66.1360%	0.5622%
Difference	+7	+31.8522	+3.5439%	+2479320	+248682000	+1.2502	+6.9824%	+33.1024	+5.6423%	+5.6423%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1861649	4094489381000850601409	22	71.794	1099694244457696 2⁵ × 4637 × 7411137619	2021-09-29	4637	7411137619	494.57	31.763	59.323
1861649	66110587706746041115380121	26	85.773	17755921687371260940 2² × 3² × 5 × 378901 × 260342436083	2020-01-27	378901	260342436083	8,144,745	1,115.8	2,083.9

exponent	prime factors	composite factor	digits	bits*
1861649	4094489381000850601409 66110587706746041115380121	270689099336997041169766477474373015262493190489	48	157.567

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-05T18:08:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.535%
2015-10-07T03:22:59	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	4.609%
2016-10-29T20:53:45	Jocelyn Larouche	low 4M	720000	720000		-		-	-	0.057	-	-	2.075%
2016-12-30T23:10:08	Jocelyn Larouche	low 4M	864000	864000		-		-	-	0.068	-	-	2.234%
2017-01-14T05:24:36	Jocelyn Larouche	low 4M	1036800	1036800		-		-	-	0.082	-	-	2.399%
2017-02-12T18:28:07	Jocelyn Larouche	low 4M	1244160	12441600	12	-		-	-	0.146	-	-	4.880%
2017-12-26T01:13:03	Jocelyn Larouche	low 4M	2488320	248832000	12	-		-	-	1.252	-	-	8.615%

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	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.062	-	-
2010-04-06T23:35:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.083	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.165	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.857	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.527	-	-
2015-05-07T05:08:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.055	-	-
2015-05-07T05:08:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.007	-	-
2015-09-10T08:47:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.014	-	-
2018-05-07T13:42:45	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.028	-	-
2019-07-01T11:11:03	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.06	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.819 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:	18.819 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.462	0.021%
25	50000	0.766	46.480%
30	250000	0.047	95.376%
35	1000000	0.002	99.783%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		84	5.813
50000	5000000	66110587706746041115380121	3	0.208
50000	6600000		73	5.697
50000	6600000	4094489381000850601409	91	7.102

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-22T17:07:00	ANONYMOUS	mcg25	50000	5000000						3	0.208
2009-07-27T19:28:00	Conductor	home	50000	5000000						3	0.208
2011-03-11T02:26:00	James Hintz	ryan	50000	5000000						3	0.208
2012-08-23T15:54:00	Bud	annan	50000	5000000						3	0.208
2013-09-24T05:40:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2014-06-10T12:48:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-01-23T16:13:00	mikr	MSI	50000	5000000						12	0.830
2016-06-15T13:30:45	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2016-09-20T02:34:46	Bruce	DESK3	50000	5000000						3	0.208
2016-11-26T17:48:20	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-01-23T12:08:41	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-08-24T06:17:36	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-12-27T15:57:57	Bruce	DESK3	50000	5000000						3	0.208
2018-02-23T13:05:09	Bruce	DESK3	50000	5000000						3	0.208
2019-11-26T06:09:05	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2019-12-01T13:43:26	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.208
2019-12-03T18:14:28	mnd9	50871b	50000	5000000						3	0.208
2019-12-07T02:09:18	IanGlencross	glenx24	50000	5000000						3	0.208
2019-12-12T02:37:32	IanGlencross	glenx24	50000	5000000						3	0.208
2019-12-17T09:02:14	Alvin Bunk	BADCAT	50000	5000000						3	0.208
2019-12-22T03:38:51	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2019-12-29T03:26:46	mnd9	50871b	50000	5000000						3	0.208
2020-01-02T21:53:29	nranks	wlaptop	50000	5000000						3	0.208
2020-01-08T18:10:23	mnd9	25836b	50000	5000000						3	0.208
2020-01-15T22:09:19	EricP	Cannonfodder	50000	5000000						3	0.208
2020-01-27T05:11:34	mnd9	kitchen	50000	5000000	66110587706746041115380121	85.773	3	2	4038300312722144	3	0.208
2021-09-29T12:11:07	TJAOI	Manual testing	50000	6600000	4094489381000850601409	71.794	91	2		91	7.102
2021-09-29T12:11:07	TJAOI	Manual testing	50000	6600000						73	5.697

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-13T00:00:00	ANONYMOUS	v4_computers	31FD6BC8A9392688	0.101
1998-12-27T00:00:00	ANONYMOUS	v4_computers	31FD6BC8A9392688	0.101
2015-06-27T00:54:00	MadPoo	Manual testing	31FD6BC8A9392688	0.101

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-01-27T14:41:43

mrh

66110587706746041115380121

023CCC3BAB28DB2E

2020-02-01T10:41:23

oodaira

com1

66110587706746041115380121

023CCC3BAB28DB2E

2021-10-01T07:55:49

JackBlock

Win10

4094489381000850601409

66110587706746041115380121

023CCC3BAB28DB2E

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 = 2488320, B2 = 248832000 (P-1 stage 2)

B1 = 2488320 (P-1 stage 1)

B1 = 1244160, B2 = 12441600 (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 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-10-01T07:55:49+00:00

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