M2178389 Mersenne number exponent details

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M2178389

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is 2 ^2178389 - 1

has 655761 decimal digits

takes 0.143 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	F8AF2EBD2C036026	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	13.6403	67.1642%	700000	21000000	0.1722	5.7161%	13.8125	69.0411%	1.8769%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8579%	0.0195	63.1530%	1.0840%
GPU72	2⁶²	0.2820	64.5161%	11000	160000	0.0018	1.5685%	0.2838	65.0727%	0.5566%
Difference	+5	+13.3583	+2.6481%	+689000	+20840000	+0.1704	+4.1476%	+13.5286	+3.9684%	+3.9684%

Known prime factors (1 factor, 96.2 bits, 0.00441604% 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
2178389	90923364099112145005957211969	29	96.199	20869404890290977645856 2⁵ × 7 × 11 × 66491 × 127381540519319	2016-10-24	66491	127381540519319	8.349e+9	661,652	1,235,781

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2010-11-05T01:17:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.238%
2010-11-08T01:30:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.418%
2011-01-14T17:43:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.487%
2014-06-21T17:25:00	Jocelyn Larouche	Manual testing	119464	119464		-		-	-	0.011	-	-	1.022%
2014-10-06T21:12:00	Jocelyn Larouche	Manual testing	148928	148928		-		-	-	0.014	-	-	1.153%
2015-12-22T14:03:57	HBendtz	Manual testing	700000	21000000	12	-		-	-	0.172	-	-	5.716%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	Dry Creek Photo	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-04T18:23:00	Sturle Sunde	gassmann.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-07T20:09:00	Sturle Sunde	golan.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.451	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.901	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.715	-	-
2016-01-02T13:50:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.430	-	-
2016-11-17T17:00:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.861	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.223 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	2.223 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	0.839	43.227%
25	50000	0.076	92.700%
30	250000	0.005	99.534%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.052
50000	5000000	90923364099112145005957211969	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-04T12:53:00	SubPrime	dijkstra	50000	5000000						3	0.256
2009-12-07T00:37:00	SubPrime	abd0	50000	5000000						3	0.256
2011-09-01T08:03:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.256
2013-05-14T22:41:00	ANONYMOUS		50000	5000000						3	0.256
2015-03-08T02:00:00	arnaud	SPR05	50000	5000000						3	0.256
2015-11-12T03:21:01	rextherunt	ocean0	50000	5000000						3	0.256
2016-03-05T20:24:30	Bruce	Desk6	50000	5000000						3	0.256
2016-06-23T14:00:50	lettp	Home	50000	5000000						3	0.256
2016-10-24T07:36:33	Bruce	Desk6	50000	5000000	90923364099112145005957211969	96.199	2	2		2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	mijutu	v4_computers	F8AF2EBD2C036026	0.143

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-10T18:40:10

kkmrkkblmbrbk

old

90923364099112145005957211969

3FE763AD726CAF__

2017-10-24T15:17:06

Oliver Kruse

GTX-2

90923364099112145005957211969

3FE763AD726CAF__

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 = 700000, B2 = 21000000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148928 (P-1 stage 1)

B1 = 119464 (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)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-10-24T15:17:06+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