M13 577 Mersenne number exponent details

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M13577

<<<

<<

is 2 ¹³⁵⁷⁷ - 1

has 4088 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	2,188.5481	79.1045%	8100000000	31521845619113850	491,130.0571	36.5826%	493,318.6052	86.7486%
Target	2⁴⁴	0.0002	68.1818%	500	50000	0.0000	1.3876%	0.0002	68.6233%
Difference	+23	+2,188.5479	+10.9227%	+8099999500	+31521845619063850	+491,130.0571	+35.1951%	+493,318.6050	+18.1253%

Known prime factors (4 factors, 278.4 bits, 2.05030070% 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
13577	81463	5	16.314	3 3	-	1	3	6.434e-13	3.171e-10	5.820e-10
13577	207429407	9	27.628	7639 7639	2008-08-26	1	7639	2.178e-9	1.193e-7	2.223e-7
13577	7175300266343596078809487	25	82.569	264244688309037198159 3² × 167 × 175811502534289553	2008-08-29	167	175811502534289553	133,649,388	2,739,241	5,116,139
13577	5174235744672422611968405354001189888272165017	46	151.858	190551511551610172054518868454046913466604 2² × 19 × 29 × 53 × 113 × 227 × 2647 × 17159 × 227444621 × 6156006246265999	2023-05-20	227444621	6156006246265999	1.192e+13	95,914	179,141

exponent	prime factors	composite factor	digits	bits*
13577	81463 207429407	16897821782441	14	43.942
13577	81463 7175300266343596078809487	584521485597148367368057239481	30	98.883
13577	207429407 7175300266343596078809487	1488368279294594192874977154384209	34	110.197
13577	81463 207429407 7175300266343596078809487	121246945136175526734174263927600817767	39	126.511
13577	81463 5174235744672422611968405354001189888272165017	42150876646824956323878220535299893186831537877987 1	51	168.172
13577	207429407 5174235744672422611968405354001189888272165017	10732886521956040316539974253160918958186914440824 54919	55	179.486
13577	81463 207429407 5174235744672422611968405354001189888272165017	87433313473810491230629592258524794109078061109289 025066497	59	195.800
13577	7175300266343596078809487 5174235744672422611968405354001189888272165017	37126695116872589163226644094639067272079254924613 929817497773369116279	71	234.427
13577	81463 7175300266343596078809487 5174235744672422611968405354001189888272165017	30244519643057917310039321078815823371853923439238 24564722821111968319436177	76	250.741
13577	207429407 7175300266343596078809487 5174235744672422611968405354001189888272165017	77011683519626768646827289911510336032805075060144 97165983181353776181867016553	79	262.055
13577	81463 207429407 7175300266343596078809487 5174235744672422611968405354001189888272165017	62736027745593554542764915180613665042403998296245 8982632487902622669103432769457039	84	278.369

11 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
2022-02-06	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 81463 skipped known factor: 207429407	-	-	1.42986e-5	-	-	0.206%
2023-02-11	USAFSS	6917th_Scty_Sq	6000000	727565939100		-	skipped known factor: 81463 skipped known factor: 207429407	-	-	11.34	-	-	14.557%
2023-05-19	JacobZ	GreatLakes	8100000000	31521845619113850			5174235744672422611968405354001189888272165017	46	151.858	491,130	5.35537e-6	982,260	36.583%

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	?	?	207429407	27.628	9	8.60579e-10	0.000	5.72906e-8

ECM factoring results:

Total ECM effort:	401.364 GHz-days
Estimated T-Level:	39.386

Digits	B1	Complete	FacMiss
20	11000	951.467	0.000%
25	50000	223.661	0.000%
30	250000	43.620	0.000%
35	1000000	6.787	0.113%
40	3000000	0.877	41.596%
45	11000000	0.098	90.698%
50	44000000	0.010	99.052%

ECM Summary

B1	B2	factor	curves	GHz-days
		7175300266343596078809487	1	0.00000e+0
50000	5000000		148	0.030
250000	25000000		551	0.567
500000	50000000		10	0.021
1000000	100000000		1,421	5.848
3000000	300000000		1,288	15.90
3000000	22972799850		1,200	379.0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-29	ANONYMOUS	Manual testing			7175300266343596078809487	82.569		1		1	-
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.010
2009-06-08	unconnected	dual5430	250000	25000000						30	0.031
2009-06-09	Rob_Dee	twopc	50000	5000000						80	0.016
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-08	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-08	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-09	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-21	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-24	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-28	Rob_Dee	twopc	250000	25000000						10	0.010
2009-07-31	Rob_Dee	twopc	500000	50000000						5	0.010
2009-08-10	Rob_Dee	twopc	500000	50000000						5	0.010
2010-06-13	James Hintz	home2	250000	25000000						481	0.495
2010-12-30	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-09	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-12	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-14	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-17	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-21	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-24	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-27	James Hintz	newestmember	1000000	100000000						3	0.012
2011-01-31	James Hintz	newestmember	1000000	100000000						3	0.012
2011-03-31	James Hintz	newestmember	1000000	100000000						3	0.012
2011-04-10	James Hintz	17_051310	1000000	100000000						11	0.045
2017-05-29	kkmrkkblmbrbk	c4.large	1000000	100000000						1380	5.679
2019-02-25	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-02-27	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-01	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-03	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-05	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-07	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-08	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-09	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-11	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-13	Corey	tab	3000000	300000000						3	0.037
2019-03-15	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-18	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-03-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-22	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-25	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-27	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-03-29	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-03-31	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-02	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-04	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-06	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-09	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-11	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-17	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-24	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-04-26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-04-28	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-04-30	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-03	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-05	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-08	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-11	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-15	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.037
2019-05-18	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-25	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-05-29	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-02	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-05	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-09	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-17	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-06-28	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.037
2019-07-08	Niels_Mache_Nextcloud		3000000	300000000						3	0.037
2019-07-21	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-07-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-12	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-19	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-24	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-08-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-08-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-03	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-08	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-09-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-09-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-07	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-12	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-22	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-10-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-10-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-06	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.037
2019-11-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2019-11-11	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.037
2021-10-10	nordi	sweet16	3000000	300000000						1000	12.35
2023-06-07	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-08	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-08	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-08	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-08	Denial140	i5-8400	3000000	22972799850						200	63.17
2023-06-08	Denial140	i5-8400	3000000	22972799850						200	63.17

Lucas-Lehmer results:
No L-L results for M13577

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

81463

207429407

7175300266343596078809487

8852C16AA96FC527

no

2017-09-21

Oliver Kruse

Manual testing

81463

207429407

7175300266343596078809487

8852C16AA96FC527

no

2017-10-02

kkmrkkblmbrbk

Manual testing

81463

207429407

7175300266343596078809487

8852C16AA96FC5__

no

2017-12-07

ATH

Manual testing

81463

207429407

7175300266343596078809487

8852C16AA96FC5__

no

2020-04-17

Oliver Kruse

Manual testing

81463

207429407

7175300266343596078809487

A7D874B1F2691B__

no

2023-05-19

JacobZ

GreatLakes

81463

207429407

7175300266343596078809487

5174235744672422611968405354001189888272165017

A7D874B1F2691B8C

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 = 8100000000, B2 = 31521845619113850 (P-1 stage 2)

B1 = 6000000, B2 = 727565939100 (P-1 stage 2)

B1 = 8100000000 (P-1 stage 1)

B1 = 6000000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

TF factor-bounds graph:

2

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=39.39 ~= 114-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