M2053067 Mersenne number exponent details

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M2053067

<<<

>>>

is 2 ^2053067 - 1

has 618035 decimal digits

takes 0.135 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	32A06DD8DE439A34	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	14.4729	68.6567%	5000000	530000000	3.2037	10.9290%	17.6766	72.0822%	3.4255%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6664%	0.0203	64.7585%	0.9654%
GPU72	2⁶²	0.2992	66.1290%	9000	120000	0.0014	1.3307%	0.3007	66.5798%	0.4507%
Difference	+5	+14.1737	+2.5277%	+4991000	+529880000	+3.2022	+9.5983%	+17.3759	+5.5025%	+5.5025%

Known prime factors (3 factors, 217.2 bits, 0.01058009% 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
2053067	5257331292746858279	19	62.189	1280360381017 1280360381017	2016-07-08	1	1280360381017	0.5887	6,650.5	12,421
2053067	2569877589090828524359	22	71.122	625863059776137 3 × 208621019925379	2021-07-13	3	208621019925379	405.15	1,083,630	2,023,919
2053067	18110492216658940886063377	26	83.905	4410594543835866264 2³ × 3 × 1783 × 3019 × 34140622693	2009-10-23	3019	34140622693	1,851,299	177.34	331.21

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
2053067	5257331292746858279 2569877589090828524359	13510697867656064984747800308214872318161	41	133.311
2053067	5257331292746858279 18110492216658940886063377	95212857457689464660655990317421112831148183	44	146.094
2053067	2569877589090828524359 18110492216658940886063377	46541748074995693923024361503823001481462300343	47	155.027
2053067	5257331292746858279 2569877589090828524359 18110492216658940886063377	24468538857381571429571306190812957642567320831861 5617193554089697	66	217.216

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.275%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.058%
2009-05-24T16:58:00	Rob_Dee	twopc	20000	280000		-		-	-	0.003	-	-	1.039%
2016-03-17T19:20:09	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.139%
2021-08-28T07:56:13	happy5214	Manual testing	5000000	530000000		-		-	-	3.204	-	-	10.929%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-08-28T08:40:42	happy5214	Manual testing	2500000	197500000	2	7			-	-	1.177

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T08:13:22	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.075	-	-
2009-01-03T04:57:00	Sturle Sunde	gorilla.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2022-03-09T08:13:22	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.150	-	-
2016-07-08T13:11:16	TJAOI	Manual testing	2⁶²	2⁶³*	5257331292746858279	62.189	19	0.289	0.274	0.588

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.836 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	0.836 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.365	69.393%
25	50000	0.034	96.681%
30	250000	0.002	99.786%

ECM Summary

B1	B2	factor	curves	GHz-days
		18110492216658940886063377	1	0.00000e+0
50000	5000000		3	0.255
50000	6750000	2569877589090828524359	6	0.582

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-11T05:07:00	ClknGo Software	plms3	50000	5000000						3	0.255
2009-10-23T20:01:00	KAMCOBILL	PC01			18110492216658940886063377	83.905		1		1	-
2021-07-13T11:57:23	happy5214	Focus	50000	6750000	2569877589090828524359	71.122	6	2	2687613134423699	6	0.582

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	32A06DD8DE439A34	0.135
1999-03-15T00:00:00	ANONYMOUS	v4_computers	32A06DD8DE439A34	0.135

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T08:31:23

Oliver Kruse

GTX-0

5257331292746858279

18110492216658940886063377

CD07F47345AE3A29

2017-10-17T21:06:41

Oliver Kruse

GTX-2

5257331292746858279

18110492216658940886063377

353548FFB54CB3__

2017-11-15T09:01:40

ATH

ec2-1xf

5257331292746858279

18110492216658940886063377

353548FFB54CB3__

2021-07-14T00:00:46

happy5214

Manual testing

5257331292746858279

2569877589090828524359

18110492216658940886063377

353548FFB54CB39B

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 = 5000000, B2 = 530000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 20000, B2 = 280000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 4000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

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10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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10¹⁰

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10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-09T08:13:22+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