M1464583 Mersenne number exponent details

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M1464583

<<<

>>>

is 2 ^1464583 - 1

has 440884 decimal digits

takes 0.056 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	BB99E2B034703857	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	20.2883	68.6567%	500000	15000000	0.0714	4.9341%	20.3597	70.2032%	1.5465%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9097%	0.0073	63.5911%	1.0911%
GPU72	2⁶⁰	0.1049	65.0000%	6500	100000	0.0006	1.4459%	0.1055	65.5061%	0.5061%
Difference	+7	+20.1834	+3.6567%	+493500	+14900000	+0.0708	+3.4882%	+20.2542	+4.6971%	+4.6971%

Known prime factors (3 factors, 211.3 bits, 0.01442700% 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
1464583	17160567345475728431	20	63.896	5858516501105 5 × 1171703300221	2017-06-06	5	1171703300221	2.0835	3,534.2	6,600.8
1464583	9746053039092618703151	22	73.045	3327245038039025 5² × 67 × 21191 × 93738613	2019-03-22	21191	93738613	1,901.2	0.2838	0.5281
1464583	24148016422890612912607	23	74.354	8243990413274841 3 × 27653 × 280927 × 353737	2009-04-03	280927	353737	4,829.4	0.0158	0.0317

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1464583	17160567345475728431 9746053039092618703151	167247799529927275468559612363426279986081	42	136.941
1464583	17160567345475728431 24148016422890612912607	414393662084668260419743006783957868229617	42	138.250
1464583	9746053039092618703151 24148016422890612912607	235347848846371525106243272321370195238524657	45	147.400
1464583	17160567345475728431 9746053039092618703151 24148016422890612912607	40387026097410007783469554403059179383122518856425 12670829423167	64	211.295

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.840%
2016-03-17T19:14:41	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 24148016422890612912607	-	-	0.071	-	-	4.934%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2022-03-08T19:02:32	LordJulius	Manual testing	2⁵⁸	2⁶¹		-	-	0.184	-	-
2022-03-09T00:17:12	LordJulius	Manual testing	2¹	2⁶¹		-	-	0.210	-	-
2022-03-08T19:02:32	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.210	-	-
2022-03-08T19:02:32	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.670	-	-
2017-06-06T15:16:59	TJAOI	Manual testing	2⁶³	2⁶⁴*	17160567345475728431	63.896	20	0.994	0.114	2.022

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.579 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.579 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
		24148016422890612912607	1	0.00000e+0
50000	5000000		213	10.10
50000	5000000	9746053039092618703151	38	1.802
250000	35000000		50	13.68

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-06T18:39:00	Steve Scott	Abit	50000	5000000						1	0.047
2009-01-12T22:33:00	Never Odd Or Even	Dad_P-1	50000	5000000						3	0.142
2009-04-03T13:40:00	axn	Manual testing			24148016422890612912607	74.354		1		1	-
2018-11-25T16:52:28	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-03-22T12:43:31	TJAOI	Manual testing	50000	5000000	9746053039092618703151	73.045	38	2		38	1.802
2019-03-22T12:43:32	TJAOI	Manual testing	50000	5000000						206	9.77
2022-01-18T14:05:44	TJAOI	Manual testing	250000	35000000						50	13.68

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	ANONYMOUS	v4_computers	BB99E2B034703857	0.056
2001-07-22T00:00:00	ANONYMOUS	v4_computers	BB99E2B034703857	0.056

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:06

alpertron

Manual testing

17160567345475728431

24148016422890612912607

779660C954F28F__

2017-10-18T07:08:41

Oliver Kruse

Threadripper

17160567345475728431

24148016422890612912607

779660C954F28F__

2019-03-22T14:56:24

ATH

ec2-PRPCF

17160567345475728431

9746053039092618703151

24148016422890612912607

8BCF5BE2848FB8AE

2019-03-23T09:24:07

kkmrkkblmbrbk

c5.large

17160567345475728431

9746053039092618703151

24148016422890612912607

8BCF5BE2848FB8AE

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 = 500000 (P-1 stage 1)

B1 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

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10⁵

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10¹

10²

10³

10⁴

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10⁶

10⁷

10⁸

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10¹³

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-09T00:17:12+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