M18 443 Mersenne number exponent details

is 2 ¹⁸⁴⁴³ - 1

has 5552 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	1,611.1217	77.6119%	400000000	400000000	0.1706	8.0187%	1,611.2923	79.4072%
Target	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.5220%	0.0001	66.4280%
Difference	+23	+1,611.1216	+11.7028%	+399999500	+399990000	+0.1706	+6.4967%	+1,611.2922	+12.9792%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
18443	36887	5	15.171	1 1	-	1	1	2.367e-13	4.265e-10	8.681e-10
18443	85317319	8	26.346	2313 3² × 257	2008-08-26	9	257	7.274e-10	9.602e-9	1.122e-8
18443	648679851793	12	39.239	17586072 2³ × 3⁴ × 7 × 3877	2008-08-26	81	3877	5.993e-6	1.228e-7	1.683e-7
18443	85242031882078121	17	56.242	2310958951420 2² × 5 × 7² × 47609 × 49531	2008-08-26	47609	49531	0.6467	2.035e-5	4.133e-5
18443	9362582970796460599985193889	28	92.919	253824837900462522365808 2⁴ × 3 × 2399 × 1509463 × 1460293526933	2009-06-08	1509463	1460293526933	7.049e+10	33.937	63.383

exponent	prime factors	composite factor	digits	bits*
18443	36887 85317319	3147099945953	13	41.517
18443	36887 648679851793	23927853693088391	17	54.410
18443	85317319 648679851793	55343625844296102967	20	65.585
18443	36887 85242031882078121	3144322830034215649327	22	71.413
18443	36887 85317319 648679851793	2041460326518550350143729	25	80.756
18443	85317319 85242031882078121	7272621626291429432277599	25	82.589
18443	648679851793 85242031882078121	55294788607800616383127920953	29	95.481
18443	36887 85317319 85242031882078121	268265193929011957468423794313	30	97.760
18443	36887 9362582970796460599985193889	345357598043769042151653846983543	33	108.090
18443	36887 648679851793 85242031882078121	2039658867375941336524439620193311	34	110.652
18443	85317319 9362582970796460599985193889	798790477983409313079868182304663591	36	119.265
18443	85317319 648679851793 85242031882078121	4717603118689291076355951049753885007	37	121.827
18443	648679851793 9362582970796460599985193889	6073318933895913709167359429910889292977	40	132.158
18443	36887 85317319 9362582970796460599985193889	29464984361374019331577097640672125881217	41	134.436
18443	36887 85317319 648679851793 85242031882078121	174018226239091879933541966372271556253209	42	136.998
18443	36887 648679851793 9362582970796460599985193889	224026515514618568990056387291122973350042599	45	147.329
18443	85242031882078121 9362582970796460599985193889	798085596095233583740956336512621012429802569	45	149.161
18443	85317319 648679851793 9362582970796460599985193889	518159288871937582721504828869365483382603168663	48	158.504
18443	36887 85242031882078121 9362582970796460599985193889	29438983383164881203452656384941051285498127362703	50	164.332
18443	36887 85317319 648679851793 9362582970796460599985193889	19113341688619161613848148622504284585534083082472 081	53	173.675
18443	85317319 85242031882078121 9362582970796460599985193889	68090523391362198043540385127318634443576430886392 511	53	175.508
18443	648679851793 85242031882078121 9362582970796460599985193889	51770204619318418061479981087309123281694194127517 0656217	57	188.400
18443	36887 85317319 85242031882078121 9362582970796460599985193889	25116551363371773992320741861914024687202038061063 60553257	58	190.679
18443	36887 648679851793 85242031882078121 9362582970796460599985193889	19096475377927984870338120623675716304918537387817 219995876479	62	203.571
18443	85317319 648679851793 85242031882078121 9362582970796460599985193889	44168950622016630363266491585399193226346304208253 001655905122223	65	214.746
18443	36887 85317319 648679851793 85242031882078121 9362582970796460599985193889	16292600815943274442098110751106200405402361233298 28472081372243439801	70	229.917

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 36887 skipped known factor: 85317319 skipped known factor: 648679851793 skipped known factor: 85242031882078121	-	-	0.171	-	-	8.019%

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	?	?	648679851793	39.239	12	2.02161e-6	0.000	4.85960e-5
2008-08-26	ANONYMOUS	Manual testing	?	?	85317319	26.346	8	2.42687e-10	0.000	6.18899e-9

ECM factoring results:

Total ECM effort:	21.658 GHz-days
Estimated T-Level:	36.207

Digits	B1	Complete	FacMiss
20	11000	424.815	0.000%
25	50000	90.148	0.000%
30	250000	15.097	0.000%
35	1000000	2.083	12.458%
40	3000000	0.241	78.547%
45	11000000	0.024	97.588%
50	44000000	0.002	99.783%

ECM Summary

B1	B2	factor	curves	GHz-days
		85242031882078121	1	0.00000e+0
		9362582970796460599985193889	1	0.00000e+0
50000	5000000		208	0.064
250000	25000000		541	0.830
1000000	100000000		1,421	8.722
3000000	300000000		654	12.04

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			85242031882078121	56.242		1		1	-
2009-04-06	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.015
2009-06-08	unconnected	dual5430			9362582970796460599985193889	92.919		1		1	-
2009-06-13	Rob_Dee	twopc	50000	5000000						140	0.043
2009-06-28	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-29	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-29	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-30	Rob_Dee	twopc	50000	5000000						6	0.002
2009-07-11	Rob_Dee	twopc	250000	25000000						10	0.015
2011-04-04	James Hintz	17_051310	250000	25000000						11	0.017
2014-09-16	James Hintz	08_04_2014	250000	25000000						520	0.798
2014-09-16	James Hintz	08_04_2014	1000000	100000000						11	0.068
2017-09-30	kkmrkkblmbrbk	r4.16xlarge-64	1000000	100000000						1410	8.654
2019-09-12	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-09-29	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-13	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-20	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-09	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2020-06-17	James Hintz	work_lappy_5_16_2019	3000000	300000000						100	1.841
2022-02-10	nordi	sweet16_ccx2	3000000	300000000						500	9.207

Lucas-Lehmer results:
No L-L results for M18443

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

5AB6613DAB392B__

2017-09-21

Oliver Kruse

Manual testing

5AB6613DAB392B__

2017-10-02

kkmrkkblmbrbk

Manual testing

36887

85317319

648679851793

85242031882078121

9362582970796460599985193889

5AB6613DAB392B__

2017-12-07

ATH

Manual testing

36887

85317319

648679851793

85242031882078121

9362582970796460599985193889

5AB6613DAB392B__

2020-04-17

Oliver Kruse

Manual testing

36887

85317319

648679851793

85242031882078121

9362582970796460599985193889

1659C8C358A74B__

2022-05-12

Jorge Coveiro

Manual testing

36887

1659C8C358A74BAA

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 = 400000000 (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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=36.21 ~= 104-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2023-03-23T17:39:31+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