M951437 Mersenne number exponent details

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M951437

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is 2 ⁹⁵¹⁴³⁷ - 1

has 286412 decimal digits

takes 0.023 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	C8A941ACB85B4ADF	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	31.2306	70.1493%	1000000	30000000	0.0907	5.7537%	31.3213	71.8668%	1.7175%
PrimeNet	2⁴⁰	0.0000	50.0000%	8000	360000	0.0010	23.4524%	0.0010	61.7262%	11.7262%
GPU72	2⁴⁴	0.0000	54.5455%	16000	650000	0.0018	18.3798%	0.0018	62.8999%	8.3544%
Difference	+23	+31.2306	+15.6038%	+984000	+29350000	+0.0889	-12.6261%	+31.3195	+8.9669%	+8.9669%

Known prime factors (1 factor, 81.5 bits, 0.00856667% 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
951437	3434729026227185733949009	25	81.506	1805021786112577992 2³ × 3³ × 919 × 379189 × 23980457	2009-09-19	379189	23980457	930,525	0.0585	0.0858

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.214%
2002-02-24T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.454%
2002-05-05T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.815%
2002-05-11T00:00:00	Jocelyn Larouche	v4_computers	5000	5000		-		-	-	0.000	-	-	0.061%
2002-05-11T00:00:00	Jocelyn Larouche	v4_computers	6000	6000		-		-	-	0.000	-	-	0.076%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.004	-	-	1.318%
2002-07-27T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.007	-	-	1.969%
2003-01-09T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.015	-	-	2.760%
2003-09-14T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.029	-	-	3.679%
2016-03-17T18:54:47	alpertron	Manual testing	200000	5000000	6	-		-	-	0.016	-	-	3.288%
unknown			1000000	30000000		-	MISSED FACTOR!	-	-	0.091	-	-	5.754%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.005	-	-
2000-11-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.010	-	-
2001-10-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.020	-	-
2003-08-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.040	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.079 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	14.079 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.692	0.000%
25	50000	1.609	20.008%
30	250000	0.131	87.737%
35	1000000	0.009	99.133%

ECM Summary

B1	B2	factor	curves	GHz-days
		3434729026227185733949009	1	0.00000e+0
50000	5000000		278	7.859
250000	25000000		44	6.219

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-12T13:27:00	James Heinrich	WHS	50000	5000000						1	0.028
2008-02-02T12:33:00	Chad Davis	Bayes	50000	5000000						3	0.085
2008-11-11T19:31:00	Sturle Sunde	v23	50000	5000000						3	0.085
2009-03-02T05:01:00	Sturle Sunde	v21	50000	5000000						3	0.085
2009-07-02T05:18:00	SubPrime	c2d0	50000	5000000						3	0.085
2009-09-19T17:45:00	JimBa	AUserv			3434729026227185733949009	81.506		1		1	-
2016-05-13T16:21:08	TJAOI	Manual testing	50000	5000000						84	2.375
2017-01-27T18:38:55	TJAOI	Manual testing	50000	5000000						90	2.544
2017-07-21T13:30:08	TJAOI	Manual testing	50000	5000000						91	2.573
2020-02-10T17:30:20	TJAOI	Manual testing	250000	25000000						44	6.219

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-12-08T00:00:00	ANONYMOUS	v4_computers	C8A941ACB85B4ADF	0.023

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T11:54:36

Oliver Kruse

GTX-1

3434729026227185733949009

E337ADC6608E02__

2017-10-15T02:43:18

Oliver Kruse

Threadripper

3434729026227185733949009

E337ADC6608E02__

2017-12-24T01:53:19

ATH

ec2-1xf

3434729026227185733949009

E337ADC6608E02__

2020-04-24T08:03:12

Oliver Kruse

AddPrpType5

3434729026227185733949009

0EC644C2C9FAC2__

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

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

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

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

B1 = 200000 (P-1 stage 1)

B1 = 131072 (P-1 stage 1)

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

B1 = 65536 (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 = 6000 (P-1 stage 1)

B1 = 5000 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-24T08:03:12+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