M811337 Mersenne number exponent details

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M811337

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is 2 ⁸¹¹³³⁷ - 1

has 244237 decimal digits

takes 0.016 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	1E54C32622210D55	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	36.6234	70.1493%	10000000	830000000	1.5834	11.1606%	38.2068	73.4808%	3.3315%
PrimeNet	2⁴⁰	0.0000	50.0000%	7000	300000	0.0007	22.3455%	0.0007	61.1727%	11.1727%
GPU72	2⁴⁴	0.0000	54.5455%	13000	500000	0.0011	17.1454%	0.0011	62.3388%	7.7934%
Difference	+23	+36.6234	+15.6038%	+9987000	+829500000	+1.5823	-5.9848%	+38.2056	+11.1420%	+11.1420%

Known prime factors (1 factor, 86.8 bits, 0.01069783% 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
811337	134285927838350258245806359	27	86.795	82755949647526402867 82755949647526402867	2009-07-19	1	82755949647526402867	31,887,484	1.306e+11	2.439e+11

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.204%
2002-02-10T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.436%
2002-03-31T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.786%
2002-05-18T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.277%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.914%
2002-11-16T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.693%
2003-07-13T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.598%
2016-03-17T18:52:12	alpertron	Manual testing	300000	10000000	12	-		-	-	0.024	-	-	3.956%
2021-09-26T15:35:49	gLauss	Manual testing	10000000	830000000		-		-	-	1.583	-	-	11.161%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-10-06T16:19:39	gLauss	Manual testing	5000000	365000000	2	7			-	-	0.777

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2000-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-10-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.024	-	-
2003-08-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.047	-	-
2008-10-11T05:35:00	Sturle Sunde	giovanni.ifi	2⁵⁸	2⁵⁹		-	-	0.047	-	-
2008-10-11T06:04:00	Sturle Sunde	giovanni.ifi	2⁵⁹	2⁶⁰		-	-	0.095	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.438 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.438 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.769	0.000%
25	50000	1.616	19.866%
30	250000	0.131	87.697%
35	1000000	0.009	99.130%

ECM Summary

B1	B2	factor	curves	GHz-days
		134285927838350258245806359	1	0.00000e+0
50000	5000000		280	6.405
250000	25000000		44	5.033

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-02T19:21:00	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-20T02:53:00	Team_Bundu	bundu3	50000	5000000						3	0.069
2008-09-29T14:52:00	Sturle Sunde	v23	50000	5000000						3	0.069
2009-01-15T22:11:00	linded	kctz73a	50000	5000000						3	0.069
2009-03-28T05:13:00	Sturle Sunde	v23	50000	5000000						3	0.069
2009-07-19T13:15:00	SubPrime	c2d0			134285927838350258245806359	86.795		1		1	-
2015-11-27T11:31:02	TJAOI	Manual testing	50000	5000000						86	1.967
2016-10-28T16:21:25	TJAOI	Manual testing	50000	5000000						90	2.059
2018-03-02T13:48:35	TJAOI	Manual testing	50000	5000000						91	2.082
2019-05-31T10:26:42	TJAOI	Manual testing	250000	25000000						44	5.033

Lucas-Lehmer results:
No L-L results for M811337

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T01:50:30

Oliver Kruse

GTX-0

134285927838350258245806359

95C9D28F8FE8BE__

2017-10-14T00:31:38

Oliver Kruse

Threadripper

95C9D28F8FE8BE__

2017-12-18T14:47:47

ATH

ec2-1xf

134285927838350258245806359

95C9D28F8FE8BE__

2020-04-21T08:53:34

Oliver Kruse

AddPrpType5

134285927838350258245806359

DE04AF496516D6__

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 = 10000000, B2 = 830000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65537 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁷

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2¹⁰⁰

Last modified: 2021-10-06T16:19:39+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