M56 123 Mersenne number exponent details

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M56123

<<<

<<

is 2 ⁵⁶¹²³ - 1

has 16895 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	529.4428	76.1194%	620000000	772483476494730	72,384.8558	30.8137%	72,914.2985	83.4779%
Target	2⁴⁴	0.0000	63.6364%	500	50000	0.0000	2.1085%	0.0000	64.4031%
Difference	+23	+529.4427	+12.4830%	+619999500	+772483476444730	+72,384.8557	+28.7052%	+72,914.2985	+19.0748%

Known prime factors (3 factors, 83.5 bits, 0.14869601% 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
56123	112247	6	16.776	1 1	-	1	1	1.556e-13	1.720e-9	3.500e-9
56123	32326849	8	24.946	288 2⁵ × 3²	2008-08-26	9	9	4.231e-11	1.548e-8	3.150e-8
56123	3647680711201	13	41.730	32497200 2⁴ × 3⁴ × 5² × 17 × 59	2008-08-26	81	81	5.355e-6	1.393e-7	2.835e-7

exponent	prime factors	composite factor	digits	bits*
56123	112247 32326849	3628591819703	13	41.723
56123	112247 3647680711201	409441216790178647	18	58.506
56123	32326849 3647680711201	117918023551207335649	21	66.676
56123	112247 32326849 3647680711201	13235944389552369804593303	26	83.453

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: 112247 skipped known factor: 32326849 skipped known factor: 3647680711201	-	-	0.350	-	-	11.231%
2023-04-23	JacobZ	GreatLakes	620000000	772483476494730		-	skipped known factor: 112247 skipped known factor: 32326849 skipped known factor: 3647680711201	-	-	72,385	-	-	30.814%

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	?	?	32326849	24.946	8	2.48252e-12	0.000	6.58760e-12
2008-08-26	ANONYMOUS	Manual testing	?	?	3647680711201	41.730	13	1.35579e-7	0.000	3.38509e-7

ECM factoring results:

Total ECM effort:	62.523 GHz-days
Estimated T-Level:	32.363

Digits	B1	Complete	FacMiss
20	11000	158.032	0.000%
25	50000	28.992	0.000%
30	250000	4.091	1.672%
35	1000000	0.473	62.337%
40	3000000	0.046	95.526%
45	11000000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	0.348
250000	25000000		584	3.613
1000000	100000000		452	11.19
1000000	3125000000	112247 32326849	1	0.268
1000000	3267412556		50	13.99
1827466	9189104925		43	33.12

	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
2010-04-30	James Hintz	02_122109	50000	5000000						11	0.014
2010-04-30	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-01	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-02	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-04	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-04	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-05	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-06	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-07	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-08	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-09	James Hintz	02_122109	50000	5000000						11	0.014
2010-05-09	James Hintz	02_122109	50000	5000000						11	0.014
2011-01-24	James Hintz	NEW_OMFG	50000	5000000						11	0.014
2011-01-28	James Hintz	home2	50000	5000000						11	0.014
2011-01-29	James Hintz	home2	50000	5000000						11	0.014
2011-02-15	James Hintz	lappy_010411	50000	5000000						11	0.014
2013-04-02	BloodIce	Mjolnir	50000	5000000						75	0.093
2013-04-02	BloodIce	Mjolnir	250000	25000000						20	0.124
2016-08-07	Ismo Laitela		250000	25000000						564	3.490
2018-10-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-10-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-10-18	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-10-22	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-10-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-10-29	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-06	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-10	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-11	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-14	Ducho_YYZ	Pantalaimon	1000000	100000000						3	0.074
2018-11-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-16	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-18	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-20	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-02	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-11	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-21	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-31	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-01-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-09	Niels_Mache_Nextcloud	SuperDry-X	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-JP	1000000	100000000						3	0.074
2019-01-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-01-19	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-22	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-01-29	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-10	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-02-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-17	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-20	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-23	Niels_Mache_Nextcloud	SuperDry-X	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-JP	1000000	100000000						3	0.074
2019-03-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-15	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-27	Niels_Mache_Nextcloud	SuperDry-JP	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-X	1000000	100000000						3	0.074
2019-04-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-04-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-04-18	Niels_Mache_Nextcloud	SuperDry-JP	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	SuperDry-JP	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-X	1000000	100000000						3	0.074
2019-05-13	Niels_Mache_Nextcloud	SuperDry-JP	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
2019-07-11	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	SuperDry3	1000000	100000000						3	0.074
2019-08-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-08-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-03	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-09-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-01	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-08	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-11-01	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-11-05	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-11-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-11-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-14	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-02-16	Niels_Mache_Nextcloud	SuperDry3	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	JoaoLima	PC	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
2020-03-02	Lin_yq		1000000	100000000						3	0.074
2020-03-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-04	Naegi Makoto	4210	1000000	100000000						3	0.074
2020-03-06	Niels_Mache_Nextcloud	SuperDry3	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	Niels_Mache_Nextcloud	SuperDry3	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
2020-03-15	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
2020-04-20	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-05-05	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-05-19	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
2021-01-23	Alex Kruppa	lily	1000000	100000000						7	0.173
2023-04-16	carlos56	Manual testing	1000000	3125000000	112247 32326849	41.723	1	2	3080936848427733	1	0.268
2023-06-21	Oliver Kruse	Krusen-NAS	1000000	3267412556						50	13.99
2023-12-01	Oliver Kruse	Krusen-NAS	1827466	9189104925						43	33.12

Lucas-Lehmer results:
No L-L results for M56123

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

112247

32326849

3647680711201

A0A9EC3B7504CA__

no

2017-09-21

Oliver Kruse

Manual testing

112247

32326849

3647680711201

A0A9EC3B7504CA__

no

2017-10-13

kkmrkkblmbrbk

Manual testing

112247

32326849

3647680711201

A0A9EC3B7504CA__

no

2020-04-17

Oliver Kruse

AddPrpType5

112247

32326849

3647680711201

A96E72C2A13161__

no

2022-05-12

Jorge Coveiro

Manual testing

112247

A96E72C2A1316196

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=32.36 ~= 91-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

JSON version of this page

Last modified: 2023-12-01T03:39:48+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