M58 231 Mersenne number exponent details

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M58231

<<<

<<

is 2 ⁵⁸²³¹ - 1

has 17530 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	unknown			600000000	301603486654470	28,262.0602	69.2626%	28,262.0602	69.2626%
Target	2⁴⁴	0.0000	63.6364%	500	50000	0.0000	2.1308%	0.0000	64.4112%
Difference	-44	0.0000	-63.6364%	+599999500	+301603486604470	+28,262.0602	+67.1318%	+28,262.0601	+4.8514%

Known prime factors (3 factors, 243.7 bits, 0.41850615% 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
58231	3843247	7	21.874	33 3 × 11	-	3	11	4.832e-12	5.909e-9	1.050e-8
58231	1399122171324450438689	22	70.245	12013550955027824 2⁴ × 59 × 149 × 85410867329	2010-05-02	149	85410867329	6,062.5	8.0032	14.948
58231	4271214608411102037568226326057401369619489457	46	151.581	36674748917338720248391976147218847088488 2³ × 55487 × 407359 × 135048811 × 364530589 × 4119873294323	2023-05-02	364530589	4119873294323	2.350e+12	386.64	721.02

exponent	prime factors	composite factor	digits	bits*
58231	3843247 1399122171324450438689	5377172087576180175140183183	28	92.119
58231	3843247 4271214608411102037568226326057401369619489457	16415332730132142672577973122941129641585993997146 879	53	173.455
58231	1399122171324450438689 4271214608411102037568226326057401369619489457	59759510571128533967388277832797380651373561591578 43938327860401873	67	221.826
58231	3843247 1399122171324450438689 4271214608411102037568226326057401369619489457	22967055972395802478456309661606503479624948646614 906242446734505917201631	74	243.700

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
2016-10-07	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 3843247	-	-	0.350	-	-	39.774%
2023-05-02	JacobZ	PM1Server	600000000	301603486654470			4271214608411102037568226326057401369619489457	46	151.581	28,262	0.000	56,524	69.263%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-05-05	ATH	colab-Pp2	15000000	1500000000	2	7			-	-	0.276

Trial Factoring results:
No TF results for M58231

ECM factoring results:

Total ECM effort:	26.525 GHz-days
Estimated T-Level:	32.211

Digits	B1	Complete	FacMiss
20	11000	141.182	0.000%
25	50000	25.547	0.000%
30	250000	3.676	2.531%
35	1000000	0.442	64.263%
40	3000000	0.046	95.510%
45	11000000	0.004	99.583%

ECM Summary

B1	B2	factor	curves	GHz-days
		1399122171324450438689	1	0.00000e+0
50000	5000000		273	0.338
250000	25000000		585	3.619
1000000	100000000		389	9.63
1000000	773000000	3843247	1	0.079
3000000	2573066252		50	12.86

	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	16_122109	50000	5000000						11	0.014
2010-04-30	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-01	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-02	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-02	James Hintz	16_122109			1399122171324450438689	70.245		1		1	-
2010-05-03	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-04	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-05	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-06	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-06	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-07	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-08	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-09	James Hintz	16_122109	50000	5000000						11	0.014
2010-05-09	James Hintz	16_122109	50000	5000000						11	0.014
2011-01-30	James Hintz	NEW_OMFG	50000	5000000						3	0.004
2011-02-10	James Hintz	lappy_010411	50000	5000000						11	0.014
2014-05-15	TJAOI	Manual testing	50000	5000000						86	0.106
2016-09-09	TJAOI	Manual testing	250000	25000000						44	0.272
2016-12-27	kkmrkkblmbrbk	x116xl	250000	25000000						541	3.347
2018-10-19	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-10-25	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-10-27	Niels_Mache_Nextcloud	SuperDry-JP	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	SuperDry3	1000000	100000000						3	0.074
2018-11-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-05	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-11-10	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-11-15	Ducho_YYZ	Pantalaimon	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-JP	1000000	100000000						3	0.074
2018-11-20	Niels_Mache_Nextcloud	SuperDry-JP	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
2018-11-26	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-11-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-04	Ducho_YYZ	Pantalaimon	1000000	100000000						3	0.074
2018-12-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-10	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-15	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-17	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2018-12-20	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-22	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2018-12-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2018-12-30	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-01-02	Niels_Mache_Nextcloud	SuperDry-X	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-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-JP	1000000	100000000						3	0.074
2019-01-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-01-26	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-01-29	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-01	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-02-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-11	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-02-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-02-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-02-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-03-03	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-03-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-03-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-19	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-22	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-03-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-04-02	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-04-06	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-04-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-04-13	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-04-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-04-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-04-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-05-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-05-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-05-10	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-05-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.074
2019-05-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-05-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-06-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.074
2019-07-03	Niels_Mache_Nextcloud		1000000	100000000						3	0.074
2019-07-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-07-30	Niels_Mache_Nextcloud	SuperDry-Y	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	SuperDry3	1000000	100000000						3	0.074
2019-08-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-08-27	Niels_Mache_Nextcloud	SuperDry3	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	SuperDry-Y	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	SuperDry3	1000000	100000000						3	0.074
2019-10-18	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-10-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.074
2019-11-04	Niels_Mache_Nextcloud	SuperDry3	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
2020-03-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-11	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-12	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
2020-03-18	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-20	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-03-22	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.074
2020-04-19	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-05-03	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-05-17	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-06-26	Alex Kruppa	lily	1000000	100000000						3	0.074
2020-12-03	Peredron	Peredron2	1000000	100000000						1	0.025
2021-01-21	Alex Kruppa	lily	1000000	100000000						7	0.173
2023-04-16	carlos56	Manual testing	1000000	773000000	3843247	21.874	1	2	635923516468341	1	0.079
2023-06-05	Naegi Makoto	12500H	3000000	2573066252						50	12.86

Lucas-Lehmer results:
No L-L results for M58231

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

3843247

1399122171324450438689

3E3D0B95454BF7__

no

2017-09-21

Oliver Kruse

Manual testing

3843247

1399122171324450438689

3E3D0B95454BF7__

no

2017-09-21

Oliver Kruse

Manual testing

3843247

1399122171324450438689

3E3D0B95454BF7__

no

2017-11-06

kkmrkkblmbrbk

c4.xlarge

3843247

1399122171324450438689

3E3D0B95454BF7__

no

2020-04-17

Oliver Kruse

AddPrpType5

3843247

1399122171324450438689

077DF269754B43__

no

2023-05-02

JacobZ

PM1Server

3843247

1399122171324450438689

4271214608411102037568226326057401369619489457

077DF269754B43B1

no

2023-05-03

ryu

pritchard

3843247

1399122171324450438689

4271214608411102037568226326057401369619489457

CE26FF499E68A183

no

2023-05-03

ryu

pritchard

3843247

1399122171324450438689

4271214608411102037568226326057401369619489457

CE26FF499E68A183

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 = 600000000, B2 = 301603486654470 (P-1 stage 2)

B1 = 600000000 (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:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=32.21 ~= 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