M2119919 Mersenne number exponent details

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M2119919

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is 2 ^2119919 - 1

has 638160 decimal digits

takes 0.139 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	FF2F77B64CD787B3	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	14.0165	67.1642%	500000	15000000	0.1230	5.1590%	14.1395	68.8582%	1.6940%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6825%	0.0198	63.0865%	1.0175%
GPU72	2⁶²	0.2898	64.5161%	10000	140000	0.0016	1.4541%	0.2914	65.0321%	0.5160%
Difference	+5	+13.7267	+2.6481%	+490000	+14860000	+0.1214	+3.7049%	+13.8481	+3.8261%	+3.8261%

Known prime factors (1 factor, 68.3 bits, 0.00322399% 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
2119919	375143201532107207431	21	68.346	88480550797485 3 × 5 × 7 × 11 × 17 × 4506266911	2015-08-07	17	4506266911	49.267	23.407	43.717

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2009-08-02T20:20:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.022%
2010-12-30T22:21:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.416%
2011-01-11T22:55:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.597%
2011-01-25T16:44:00	James Heinrich	i7-920	140000	3010000		-		-	-	0.028	-	-	3.103%
2016-03-28T23:19:12	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.159%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
1999-07-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T09:12:34	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.072	-	-
2009-01-03T11:26:00	Sturle Sunde	giovanni.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-02T05:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.145	-	-
2013-09-06T08:31:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.463	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.926	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.763	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.363 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	1.363 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.516	59.683%
25	50000	0.047	95.442%
30	250000	0.003	99.713%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.278
50000	5000000	375143201532107207431	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-17T09:27:00	dachshund	Ann	50000	5000000						3	0.256
2009-11-17T06:17:00	KAMCOBILL	PC01	50000	5000000						3	0.256
2011-07-13T17:46:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-15T01:04:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.256
2014-11-20T12:31:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2015-08-07T01:29:00	guru	w6	50000	5000000	375143201532107207431	68.346	1	2		1	0.085

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	FF2F77B64CD787B3	0.139
1999-07-12T00:00:00	ANONYMOUS	v4_computers	FF2F77B64CD787B3	0.139

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T06:39:11

Oliver Kruse

GTX-2

375143201532107207431

19D03605BE7013__

2017-11-17T17:01:24

kkmrkkblmbrbk

c4.xlarge

375143201532107207431

19D03605BE7013__

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

B1 = 500000 (P-1 stage 1)

B1 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

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10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-09T09:12:34+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