M798227 Mersenne number exponent details

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M798227

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is 2 ⁷⁹⁸²²⁷ - 1

has 240291 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	60F13B1395149D__	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	37.2249	70.1493%	500000	15000000	0.0374	4.5825%	37.2623	71.5172%	1.3679%
PrimeNet	2⁴⁰	0.0000	50.0000%	7000	300000	0.0007	22.3068%	0.0007	61.1534%	11.1534%
GPU72	2⁴⁴	0.0000	54.5455%	13000	500000	0.0011	17.1143%	0.0011	62.3247%	7.7792%
Difference	+23	+37.2249	+15.6038%	+487000	+14500000	+0.0362	-12.5318%	+37.2611	+9.1925%	+9.1925%

Known prime factors (1 factor, 63.1 bits, 0.00790680% 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
798227	9983262943688734591	19	63.114	6253398434085 3 × 5 × 11 × 37899384449	2008-01-19	11	37899384449	3.4928	59.798	111.69

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	-	-	0.203%
2002-02-10T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.434%
2002-03-31T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.783%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.273%
2002-07-27T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.909%
2002-12-16T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.686%
2003-07-30T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.590%
unknown			500000	15000000		-		-	-	0.037	-	-	4.583%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-10-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-02-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-12-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.024	-	-
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.048	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.396 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:	11.396 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
		9983262943688734591	1	0.00000e+0
50000	5000000		279	6.372
250000	25000000		44	5.024

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-02T04:40:00	Chad Davis	Bayes	50000	5000000						1	0.023
2008-01-19T00:42:00	Team_Bundu	bundu3			9983262943688734591	63.114		1		1	-
2015-09-13T11:37:00	Richard B. Woods	Puttputt	50000	5000000						2	0.046
2015-12-04T11:31:41	TJAOI	Manual testing	50000	5000000						95	2.170
2016-09-09T13:50:59	TJAOI	Manual testing	50000	5000000						90	2.055
2017-08-04T10:34:51	TJAOI	Manual testing	50000	5000000						91	2.078
2019-04-12T15:20:20	TJAOI	Manual testing	250000	25000000						44	5.024

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-11-24T00:00:00	ANONYMOUS	v4_computers	60F13B1395149D__	0.016

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T01:08:21

Oliver Kruse

GTX-0

9983262943688734591

29D662BE4B83BD__

2017-10-13T22:48:13

Oliver Kruse

Threadripper

29D662BE4B83BD__

2017-12-17T15:53:39

ATH

ec2-1xf

9983262943688734591

29D662BE4B83BD__

2020-04-21T06:28:48

Oliver Kruse

AddPrpType5

9983262943688734591

6F4F093878ADC1__

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)

10⁰

10¹

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10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-21T06:28:48+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