M56 519 Mersenne number exponent details

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M56519

<<<

<<

is 2 ⁵⁶⁵¹⁹ - 1

has 17014 decimal digits

takes 0.000 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	-unknown-	-unknown-
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	525.7332	76.1194%	620000000	772483476494730	72,384.8558	30.8229%	72,910.5890	83.4801%
Target	2⁴⁴	0.0000	63.6364%	500	50000	0.0000	2.1128%	0.0000	64.4046%
Difference	+23	+525.7332	+12.4830%	+619999500	+772483476444730	+72,384.8557	+28.7101%	+72,910.5890	+19.0754%

Known prime factors (3 factors, 201.0 bits, 0.35556497% 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
56519	113039	6	16.786	1 1	-	1	1	1.545e-13	1.720e-9	3.500e-9
56519	5595833153	10	32.382	49504 2⁵ × 7 × 13 × 17	2008-08-26	32	32	1.736e-8	5.504e-8	1.120e-7
56519	4947966575637683706651849616166599793282610751	46	151.794	43772594841006420023813669882398837499625 3 × 5³ × 31 × 457 × 1503263 × 1793497 × 13682791 × 223348384030697	2023-04-24	13682791	223348384030697	2.828e+12	20,928	39,088

exponent	prime factors	composite factor	digits	bits*
56519	113039 5595833153	632547383781967	15	49.168
56519	113039 4947966575637683706651849616166599793282610751	55931319374350812851621842876185627403287303668228 9	51	168.580
56519	5595833153 4947966575637683706651849616166599793282610751	27687995403889232601810346710915383894533779938840 027903	56	184.175
56519	113039 5595833153 4947966575637683706651849616166599793282610751	31298233124602349640760397818551640800542039505065 37914127217	61	200.962

4 Composite Factors:

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-10-02	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 113039 skipped known factor: 5595833153	-	-	0.350	-	-	11.237%
2023-04-24	JacobZ	GreatLakes	620000000	772483476494730			4947966575637683706651849616166599793282610751	46	151.794	72,385	0.000	144,770	30.823%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-05-03	ATH	colab-Pp2	15000000	1500000000	2	7			-	-	0.176

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	5595833153	32.382	10	7.23981e-9	0.000	1.91446e-8

ECM factoring results:

Total ECM effort:	25.408 GHz-days
Estimated T-Level:	32.091

Digits	B1	Complete	FacMiss
20	11000	147.523	0.000%
25	50000	26.456	0.000%
30	250000	3.669	2.549%
35	1000000	0.418	65.829%
40	3000000	0.040	96.075%
45	11000000	0.003	99.674%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	0.348
250000	25000000		585	3.619
1000000	100000000		440	10.89
1000000	2187000000	113039	1	0.193
1000000	2366257530		50	10.36

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-20	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.037
2010-04-29	James Hintz	03_122109	50000	5000000						11	0.014
2010-04-30	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-01	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-02	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-02	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-03	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-04	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-05	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-06	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-06	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-07	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-08	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-09	James Hintz	03_122109	50000	5000000						11	0.014
2010-05-09	James Hintz	03_122109	50000	5000000						11	0.014
2011-02-21	James Hintz	lappy_010411	50000	5000000						11	0.014
2014-05-08	TJAOI	Manual testing	50000	5000000						86	0.106
2016-08-19	TJAOI	Manual testing	250000	25000000						44	0.272
2016-12-23	kkmrkkblmbrbk	x116xl	250000	25000000						541	3.347
2018-10-15	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-10-17	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-10-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-10-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-10-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-29	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-11	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-13	Ducho_YYZ	Pantalaimon	1000000	100000000						3	0.074
2018-11-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-17	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-22	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-27	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-29	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-15	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-18	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-21	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-15	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-22	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-28	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-10	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-03-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-15	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-03-20	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-27	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-03-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-04-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-04-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-04-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-04-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-04-18	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-04-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-04-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-05-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-05-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-05-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-05-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-05-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-05-22	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-05-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-03	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-07-15	Niels_Mache_Nextcloud		1000000	100000000						3	0.074
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-07-27	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-07-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-08-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-16	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-20	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-08-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-08	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-09-16	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-20	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-09-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-21	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-25	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-11-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-11-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2020-02-17	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-20	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-22	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-27	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-06	Naegi Makoto	4210	1000000	100000000						3	0.074
2020-03-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-10	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-11	Naegi Makoto	4210	1000000	100000000						3	0.074
2020-03-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-16	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-17	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-21	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-22	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-04-21	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-05-06	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-05-20	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-07-18	Meng-Hsuan Wu	MacBook_Pro_2016	1000000	100000000						3	0.074
2020-12-03	Peredron	Peredron2	1000000	100000000						1	0.025
2021-01-25	Alex Kruppa	lily	1000000	100000000						7	0.173
2023-04-16	carlos56	Manual testing	1000000	2187000000	113039	16.786	1	2	8706309450661003	1	0.193
2023-06-13	Oliver Kruse	Krusen-NAS	1000000	2366257530						50	10.36

Lucas-Lehmer results:
No L-L results for M56519

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

113039

5595833153

E634158ABA8257__

no

2017-09-21

Oliver Kruse

Manual testing

113039

5595833153

E634158ABA8257__

no

2017-10-13

kkmrkkblmbrbk

Manual testing

113039

5595833153

E634158ABA8257__

no

2020-04-17

Oliver Kruse

AddPrpType5

113039

5595833153

B68A1017DC2401__

no

2022-05-12

Jorge Coveiro

Manual testing

113039

B68A1017DC2401C7

no

2023-04-24

JacobZ

GreatLakes

113039

5595833153

4947966575637683706651849616166599793282610751

B68A1017DC2401C7

no

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 = 620000000, B2 = 772483476494730 (P-1 stage 2)

B1 = 620000000 (P-1 stage 1)

B1 = 100000000, B2 = 2000000000 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=32.09 ~= 90-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

2¹⁶⁰

Last modified: 2023-09-25T11:53:03+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