M2191811 Mersenne number exponent details

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M2191811

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is 2 ^2191811 - 1

has 659801 decimal digits

takes 0.144 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	F89F515710145EAB	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	13.5568	67.1642%	500000	15000000	0.1230	5.1797%	13.6798	68.8650%	1.7008%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8611%	0.0194	63.1542%	1.0853%
GPU72	2⁶²	0.2803	64.5161%	11000	160000	0.0018	1.5704%	0.2821	65.0734%	0.5573%
Difference	+5	+13.2765	+2.6481%	+489000	+14840000	+0.1212	+3.6093%	+13.3977	+3.7916%	+3.7916%

Known prime factors (1 factor, 77.4 bits, 0.00352924% 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
2191811	193175849044280903202823	24	77.354	44067633806993601 3 × 7² × 197 × 1521724983839	2015-12-15	197	1521724983839	22,915	7,904.2	14,763

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.238%
2010-11-09T10:50:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.419%
2011-01-11T22:23:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.490%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	119284	119284		-		-	-	0.011	-	-	1.023%
2014-10-12T23:56:00	Jocelyn Larouche	Manual testing	148568	148568		-		-	-	0.014	-	-	1.153%
2016-04-02T16:17:37	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.180%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T16:35:58	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.070	-	-
2009-01-03T03:17:00	Sturle Sunde	gigi.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-09T16:10:00	Sturle Sunde	gideon.ifi	2⁶¹	2⁶²		-	-	0.140	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.448	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.896	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.705	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.369 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:	1.369 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	1.284
50000	5000000	193175849044280903202823	1	0.086

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-23T06:04:00	dragon325	x-liberty	50000	5000000						3	0.257
2009-12-13T10:03:00	KAMCOBILL	PC01	50000	5000000						3	0.257
2011-09-05T19:11:00	S36049	Wolle5	50000	5000000						3	0.257
2013-05-23T16:42:00	hiems	Laptop	50000	5000000						3	0.257
2015-03-07T18:13:00	Jason U	Server7	50000	5000000						3	0.257
2015-12-15T20:19:25	guru	w1	50000	5000000	193175849044280903202823	77.354	1	2		1	0.086

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-11-21T00:00:00	DL	v4_computers	F89F515710145EAB	0.144
1998-03-23T00:00:00	ANONYMOUS	v4_computers	F89F515710145EAB	0.144
1999-02-14T00:00:00	ANONYMOUS	v4_computers	F89F515710145EAB	0.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:30:59

alpertron

Manual testing

193175849044280903202823

D62A667614F2C0__

2017-10-25T01:02:13

Oliver Kruse

GTX-3

193175849044280903202823

D62A667614F2C0__

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 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148568 (P-1 stage 1)

B1 = 119284 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-09T16:35:58+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