M2718281 Mersenne number exponent details

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M2718281

<<<

>>>

is 2 ^2718281 - 1

has 818285 decimal digits

takes 0.210 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	10.9311	67.1642%	600000	891581460	5.5037	9.7589%	16.4348	70.3686%	3.2044%
PrimeNet	2⁵⁹	0.0283	62.7119%	12000	220000	0.0026	2.8465%	0.0309	63.7733%	1.0614%
GPU72	2⁶³	0.5871	65.0794%	14000	220000	0.0028	1.6634%	0.5900	65.6603%	0.5809%
Difference	+4	+10.3440	+2.0848%	+586000	+891361460	+5.5008	+8.0954%	+15.8448	+4.7083%	+4.7083%

Known prime factors (4 factors, 181.4 bits, 0.00667290% 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
2718281	233772167	9	27.801	43 43	-	1	43	6.639e-12	3.683e-7	4.742e-7
2718281	7475272751	10	32.799	1375 5³ × 11	2008-09-07	125	125	2.731e-10	1.400e-5	2.849e-5
2718281	1298446721833	13	40.240	238836 2² × 3 × 13 × 1531	2008-09-30	13	1531	9.139e-8	1.072e-5	1.750e-5
2718281	1767919131835490671793809	25	80.548	325190650237317384 2³ × 3 × 13 × 307 × 337 × 1873 × 5378701	2019-07-21	1873	5378701	178,291	0.0330	0.0613

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
2718281	233772167 7475272751	1747510709917321417	19	60.600
2718281	233772167 1298446721833	303540703896946622111	21	68.040
2718281	7475272751 1298446721833	9706243398343501672583	22	73.039
2718281	233772167 7475272751 1298446721833	2269049552660204596367852397361	31	100.840
2718281	233772167 1767919131835490671793809	413290286529941341853524507114103	33	108.349
2718281	7475272751 1767919131835490671793809	13215677712181420033574944708198559	35	113.348
2718281	1298446721833 1767919131835490671793809	2295548801197636211035722213754531897	37	120.788
2718281	233772167 7475272751 1767919131835490671793809	3089457617150252858386027581340759803707353	43	141.148
2718281	233772167 1298446721833 1767919131835490671793809	536635417710223612331490096319434127632310799	45	148.589
2718281	7475272751 1298446721833 1767919131835490671793809	17159853402183406133966219752084649692404438647	47	153.588
2718281	233772167 7475272751 1298446721833 1767919131835490671793809	40114961152307373833783754962430313260292690629277 38049	55	181.388

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-01-04T08:21:45	Denial140	i5-8400	600000	891581460		-	skipped known factor: 233772167 skipped known factor: 7475272751 skipped known factor: 1298446721833 skipped known factor: 1767919131835490671793809	-	-	5.504	-	-	9.759%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:37:00	markr	Manual testing	?	?	1298446721833	40.240	13	3.75097e-8	0.455	8.12672e-8
2008-09-07T19:41:00	Will Edgington	Manual testing	?	?	7475272751	32.799	10	6.26455e-11	0.455	1.35726e-10

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.508 GHz-days
Estimated T-Level:	2.700

Digits	B1	Curves	Complete	FacMiss
20	11000	54 / 100	0.540	58.117%
25	50000	54 / 280	0.193	82.432%
30	250000	48 / 640	0.075	92.769%

New Calculation Method

Total ECM effort:	25.508 GHz-days
Estimated T-Level:	2.700

Digits	B1	Complete	FacMiss
20	11000	4.194	1.509%
25	50000	0.596	55.112%
30	250000	0.063	93.848%
35	1000000	0.005	99.477%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.622
250000	25000000	1767919131835490671793809	48	24.89

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-04-14T05:26:56	alpertron		50000	5000000						3	0.311
2018-09-28T16:57:51	alpertron	Manual testing	50000	5000000						3	0.311
2019-07-21T12:09:56	nordi	nordiputer	250000	25000000	1767919131835490671793809	80.548	48	2		48	24.89

Lucas-Lehmer results:
No L-L results for M2718281

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-19T20:59:53

Oliver Kruse

GTX-1

233772167

7475272751

1298446721833

623BA5F1BC758A__

2017-12-05T01:00:12

kkmrkkblmbrbk

c4.xlarge

233772167

7475272751

1298446721833

623BA5F1BC758A__

2019-07-22T21:47:23

nordi

nordiputer

708E7A5808990B__

2019-07-27T00:59:08

Brett Walker

brain

233772167

7475272751

1298446721833

1767919131835490671793809

623BA5F1BC758A6C

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 = 600000, B2 = 891581460 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-04T08:21:45+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