M791419 Mersenne number exponent details

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M791419

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is 2 ⁷⁹¹⁴¹⁹ - 1

has 238241 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	E5C179E2A84DEF93	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	37.5451	70.1493%	500000	15000000	0.0374	4.5777%	37.5825	71.5157%	1.3665%
PrimeNet	2⁴⁰	0.0000	50.0000%	7000	300000	0.0007	22.2865%	0.0007	61.1433%	11.1433%
GPU72	2⁴⁴	0.0000	54.5455%	13000	500000	0.0011	17.0980%	0.0011	62.3173%	7.7718%
Difference	+23	+37.5451	+15.6038%	+487000	+14500000	+0.0362	-12.5202%	+37.5813	+9.1985%	+9.1985%

Known prime factors (1 factor, 63.1 bits, 0.00797507% 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
791419	9997338476106485279	19	63.116	6316084448381 5651 × 1117693231	2009-09-14	5651	1117693231	4.4228	1.7637	3.2937

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	-	-	0.203%
2002-02-03T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.433%
2002-03-31T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.782%
2002-05-18T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.271%
2002-07-27T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.906%
2002-12-09T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.682%
2003-07-30T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.586%
unknown			500000	15000000		-		-	-	0.037	-	-	4.578%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-10-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-02-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-12-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.024	-	-
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.049	-	-
2008-10-12T08:25:00	Sturle Sunde	tristan.ifi	2⁵⁸	2⁵⁹		-	-	0.049	-	-
2008-10-12T08:56:00	Sturle Sunde	tristan.ifi	2⁵⁹	2⁶⁰		-	-	0.097	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.386 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	323 / 100	3.230	3.892%
25	50000	323 / 280	1.154	31.486%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.386 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.731	0.000%
25	50000	1.613	19.937%
30	250000	0.131	87.717%
35	1000000	0.009	99.131%

ECM Summary

B1	B2	factor	curves	GHz-days
		9997338476106485279	1	0.00000e+0
50000	5000000		279	6.366
250000	25000000		44	5.020

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-01T17:56:00	Team_Bundu	bundu1	50000	5000000						1	0.023
2008-01-18T19:46:00	Steve Scott	Asus-2	50000	5000000						3	0.068
2008-09-24T00:47:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-01-06T01:16:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-03-21T03:34:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-07-11T07:49:00	Architects Cubed	m1_01	50000	5000000						3	0.068
2009-09-14T10:08:00	JimBa	Dmansrvr			9997338476106485279	63.116		1		1	-
2015-11-20T11:54:59	TJAOI	Manual testing	50000	5000000						82	1.871
2016-09-09T13:49:48	TJAOI	Manual testing	50000	5000000						90	2.054
2017-08-04T10:34:24	TJAOI	Manual testing	50000	5000000						91	2.076
2019-12-16T13:24:17	TJAOI	Manual testing	250000	25000000						44	5.020

Lucas-Lehmer results:
No L-L results for M791419

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T00:44:02

Oliver Kruse

GTX-2

9997338476106485279

D2537D930F2638__

2017-10-13T22:01:15

Oliver Kruse

GTX-2

D2537D930F2638__

2017-12-17T04:41:35

ATH

ec2-1xf

9997338476106485279

D2537D930F2638__

2020-04-21T05:09:01

Oliver Kruse

AddPrpType5

9997338476106485279

25A2C6A7019568__

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

B1 = 500000 (P-1 stage 1)

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

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)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-21T05:09:01+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