M2713453 Mersenne number exponent details

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M2713453

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>>>

is 2 ^2713453 - 1

has 816831 decimal digits

takes 0.210 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	A43F6DB9C601813F	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	10.9506	67.1642%	2700000	84000000	0.7984	8.3180%	11.7490	69.8955%	2.7313%
PrimeNet	2⁵⁹	0.0283	62.7119%	12000	220000	0.0026	2.8456%	0.0309	63.7729%	1.0611%
GPU72	2⁶³	0.5882	65.0794%	14000	220000	0.0028	1.6629%	0.5910	65.6601%	0.5807%
Difference	+4	+10.3624	+2.0848%	+2686000	+83780000	+0.7956	+6.6552%	+11.1580	+4.2354%	+4.2354%

Known prime factors (1 factor, 72.3 bits, 0.00266605% 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
2713453	5985340445974706145841	22	72.342	1102901072171640 2³ × 3 × 5 × 7² × 37 × 5069411069	2017-07-15	49	5069411069	608.81	30.932	57.772

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.298%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.921%
2010-12-19T21:41:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.320%
2010-12-26T20:13:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.439%
2011-01-18T00:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.628%
2011-04-21T13:17:00	James Heinrich	WHS	185000	4578750		-		-	-	0.048	-	-	3.681%
2016-09-18T15:37:54	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	8.318%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-27T00:25:00	Sturle Sunde	gimba.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-04-23T17:25:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.113	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.362	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.724	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.377	-	-
2016-01-30T15:58:42	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.754	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.281 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

New Calculation Method

Total ECM effort:	2.281 GHz-days
Estimated T-Level:	1.100

Digits	B1	Complete	FacMiss
20	11000	0.710	49.180%
25	50000	0.064	93.787%
30	250000	0.004	99.606%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	2.177
50000	5000000	5985340445974706145841	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-10T08:50:00	Never Odd Or Even	C_Quad	50000	5000000						3	0.311
2010-08-19T19:33:00	Kamil_Górski	thefault	50000	5000000						3	0.311
2013-01-26T23:02:00	Brian V.	dxl5420	50000	5000000						3	0.311
2015-02-20T13:26:00	Jason U	Server7	50000	5000000						3	0.311
2016-02-05T04:43:18	Jason U	Server7	50000	5000000						3	0.311
2016-05-01T12:49:30	lettp	Home	50000	5000000						3	0.311
2016-11-15T20:31:42	S36049	Wolle5	50000	5000000						3	0.311
2017-07-15T18:48:48	Bruce	eleven	50000	5000000	5985340445974706145841	72.342	1	2		1	0.104

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	A43F6DB9C601813F	0.210

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:41

alpertron

Manual testing

5985340445974706145841

6812827CB0D787__

2017-11-15T09:52:03

Oliver Kruse

GTX-0

5985340445974706145841

6812827CB0D787__

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 185000, B2 = 4578750 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-11-15T09:52:03+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