M4441111 Mersenne number exponent details

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M4441111

<<<

>>>

is 2 ^4441111 - 1

has 1336908 decimal digits

takes 0.554 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	F4F3AFA11775F579	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	6.6906	65.6716%	12000000	12000000	2.1702	6.2346%	8.8608	67.8119%	2.1403%
PrimeNet	2⁶¹	0.0692	62.2951%	18000	360000	0.0066	2.9422%	0.0758	63.4044%	1.1094%
GPU72	2⁶⁵	1.6428	64.6154%	26000	550000	0.0099	2.0862%	1.6526	65.3536%	0.7382%
Difference	+2	+5.0479	+1.0563%	+11974000	+11450000	+2.1603	+4.1484%	+7.2082	+2.4583%	+2.4583%

Known prime factors (1 factor, 103.7 bits, 0.00233408% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4441111	16012105959687734439631172715623	32	103.659	1802714001033495271749701 434743 × 530249 × 812807 × 9621149	2017-10-28	812807	9621149	4.330e+10	0.2338	0.2992

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-04-15T00:00:00	ANONYMOUS	v4_computers	25000	300000		-		-	-	0.007	-	-	1.318%
2011-07-06T16:54:00	harlee	P4_2600	50000	812500		-		-	-	0.017	-	-	2.073%
2014-08-22T20:27:00	Jocelyn Larouche	Manual testing	64452	64452		-		-	-	0.012	-	-	0.814%
2014-12-02T02:14:00	Nesowa	newfs	255000	5482500		-		-	-	0.098	-	-	4.272%
2017-10-28T08:44:32	mikr	S065	9000000	9000000		-		-	-	1.628	-	-	5.801%
2017-10-28T13:20:10	mikr	S065	12000000	12000000			16012105959687734439631172715623	32	103.659	2.170	1.108	4.340	6.235%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-04-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.069	-	-
2010-04-03T13:19:00	Architects Cubed	Manual testing	2⁶¹	2⁶²		-	-	0.069	-	-
2012-02-03T03:48:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.359	-	-
2016-02-23T16:38:51	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.221	-	-
2014-09-07T23:02:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.442	-	-
2014-09-13T18:29:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.841	-	-
2015-06-23T21:45:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.683	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

51.764 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	281 / 100	2.810	5.936%
25	50000	281 / 280	1.004	36.591%

New Calculation Method

Total ECM effort:

51.764 GHz-days

Digits	B1	Complete	FacMiss
20	11000	9.065	0.012%
25	50000	0.819	44.077%
30	250000	0.050	95.080%
35	1000000	0.002	99.769%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	51.76

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-31T20:59:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.553
2013-09-11T04:24:00	S00030	op9020-usff	50000	5000000						3	0.553
2016-09-19T07:48:16	ethanmyers	ethan	50000	5000000						3	0.553
2017-09-13T15:48:36	mikr	MSI	50000	5000000						131	24.13
2017-10-18T13:00:22	mikr	S051	50000	5000000						141	25.97

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-02-16T00:00:00	ANONYMOUS	v4_computers	058C54884FBBCD__	0.554
2001-04-15T00:00:00	ANONYMOUS	v4_computers	F4F3AFA11775F579	0.554

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-29T17:20:09

YarBer

Manual testing

16012105959687734439631172715623

66D2B1B111B3BB__

2017-10-30T05:05:37

YarBer

Manual testing

16012105959687734439631172715623

66D2B1B111B3BB__

2018-03-16T18:11:55

kkmrkkblmbrbk

c5.large

16012105959687734439631172715623

66D2B1B111B3BB__

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 = 12000000 (P-1 stage 1)

B1 = 9000000 (P-1 stage 1)

B1 = 255000, B2 = 5482500 (P-1 stage 2)

B1 = 255000 (P-1 stage 1)

B1 = 50000, B2 = 812500 (P-1 stage 2)

B1 = 64452 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 25000, B2 = 300000 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2018-03-16T18:11:55+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