M14 281 Mersenne number exponent details

is 2 ¹⁴²⁸¹ - 1

has 4300 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	2,080.6608	79.1045%	400000000	400000000	0.1382	7.8512%	2,080.7991	80.7450%
Target	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.4090%	0.0002	68.6301%
Difference	+23	+2,080.6607	+10.9227%	+399999500	+399990000	+0.1382	+6.4422%	+2,080.7989	+12.1149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
14281	13938257	8	23.733	488 2³ × 61	-	8	61	8.652e-11	3.763e-9	5.627e-9
14281	1805661079	10	30.750	63219 3 × 13 × 1621	2008-08-26	13	1621	1.687e-8	3.477e-8	5.699e-8
14281	148073604347344927871	21	67.005	5184286966856135 5 × 1151 × 1237 × 19751 × 36871	2008-08-26	19751	36871	2,178.1	7.148e-6	1.389e-5
14281	9966065908771335003475470943081	31	102.975	348927452866442651196536340 2² × 3 × 5 × 43 × 18047 × 61073851 × 122702980109	2013-04-04	61073851	122702980109	1.127e+13	2.3302	4.3150
14281	694177295826160448071403167254080687	36	119.063	24304225748412591837805586697503 19 × 23 × 437366471 × 127161273017402306789	2019-04-30	437366471	127161273017402306789	9.421e+12	2.394e+9	4.472e+9

exponent	prime factors	composite factor	digits	bits*
14281	13938257 1805661079	25167768173999303	17	54.482
14281	13938257 148073604347344927871	2063887952309610872312460847	28	90.737
14281	1805661079 148073604347344927871	267370744197245933244727032809	30	97.755
14281	13938257 1805661079 148073604347344927871	3726682146902472509769849278139273913	37	121.487
14281	13938257 9966065908771335003475470943081	138909587915393421511537007200695349817	39	126.707
14281	1805661079 9966065908771335003475470943081	17995337322217164326645987613116786044399	41	133.725
14281	13938257 694177295826160448071403167254080687	9675621552790051648454371695801360914142559	43	142.795
14281	1805661079 694177295826160448071403167254080687	1253448924998767071091733312028020800441481273	46	149.813
14281	13938257 1805661079 9966065908771335003475470943081	250823636398754646196023723370438334900846672543	48	157.457
14281	148073604347344927871 9966065908771335003475470943081	14757113002749692300957769311538475229662262915105 51	52	169.980
14281	13938257 1805661079 694177295826160448071403167254080687	17470893253006540120013849478507745117899079443761 161	53	173.545
14281	148073604347344927871 694177295826160448071403167254080687	10278933424907269777661104650256108521851555335642 9127377	57	186.068
14281	13938257 148073604347344927871 9966065908771335003475470943081	20568843361036691796167073481093633313916664371230 978049607	59	193.712
14281	1805661079 148073604347344927871 9966065908771335003475470943081	26646344587469939367065398468505650333206734460871 10058544529	61	200.730
14281	13938257 148073604347344927871 694177295826160448071403167254080687	14327041576224772732937333551916475639745709411791 21779666361889	64	209.800
14281	1805661079 148073604347344927871 694177295826160448071403167254080687	18560270018987226221675640319113362539907574485185 1889726582259783	66	216.818
14281	9966065908771335003475470943081 694177295826160448071403167254080687	69182166825761715829510799450976354480957862160306 55182393558376647	67	222.038
14281	13938257 1805661079 148073604347344927871 9966065908771335003475470943081	37140359897071499467257485966143816029637109904637 784383278691145953	68	224.462
14281	13938257 1805661079 148073604347344927871 694177295826160448071403167254080687	25869781351403883879485404540736405921540452942115 38564944763268496218231	73	240.550
14281	13938257 9966065908771335003475470943081 694177295826160448071403167254080687	96427882103434101599268970702316732967869228896092 791810583291798208684279	74	245.770
14281	1805661079 9966065908771335003475470943081 694177295826160448071403167254080687	12491954599816290480160585017880257183557285834191 239933717694421025910422113	77	252.788
14281	13938257 1805661079 9966065908771335003475470943081 694177295826160448071403167254080687	17411607364457160949913163524956461985051762417941 6889344820190287725343122389477041	84	276.520
14281	148073604347344927871 9966065908771335003475470943081 694177295826160448071403167254080687	10244052798449852054153205841061917695291908269926 65314844495483467873609259480065828537	88	289.043
14281	13938257 148073604347344927871 9966065908771335003475470943081 694177295826160448071403167254080687	14278424062636323954276530038662216174982630748666 306273288493083914473609376212843895066640009	95	312.775
14281	1805661079 148073604347344927871 9966065908771335003475470943081 694177295826160448071403167254080687	18497287429381929387492644090280964811489980306644 78377487986431889227323131097166642947148411423	97	319.792
14281	13938257 1805661079 148073604347344927871 9966065908771335003475470943081 694177295826160448071403167254080687	25781994599359468295872505893986728975050389843895 38039637056930018504596122327700064122459197555550 9711	104	343.525

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: 13938257 skipped known factor: 1805661079 skipped known factor: 148073604347344927871	-	-	0.138	-	-	7.851%

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	?	?	1805661079	30.750	10	6.84877e-9	0.000	3.44578e-7

ECM factoring results:

Total ECM effort:	24.814 GHz-days
Estimated T-Level:	36.702

Digits	B1	Complete	FacMiss
20	11000	494.700	0.000%
25	50000	114.192	0.000%
30	250000	19.661	0.000%
35	1000000	2.826	5.925%
40	3000000	0.340	71.154%
45	11000000	0.036	96.511%
50	44000000	0.003	99.672%

ECM Summary

B1	B2	factor	curves	GHz-days
		148073604347344927871	1	0.00000e+0
		9966065908771335003475470943081	1	0.00000e+0
50000	5000000		148	0.037
250000	25000000		551	0.685
500000	50000000		10	0.025
1000000	100000000		1,372	6.823
3000000	300000000		243	3.625
3000000	300000000	694177295826160448071403167254080687	2	0.030
3000000	427859251		800	13.59

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			148073604347344927871	67.005		1		1	-
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.012
2009-06-08	unconnected	dual5430	250000	25000000						30	0.037
2009-06-10	Rob_Dee	twopc	50000	5000000						80	0.020
2009-07-06	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-06	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-07	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-08	Rob_Dee	twopc	250000	25000000						10	0.012
2009-08-05	Rob_Dee	twopc	500000	50000000						5	0.012
2009-08-12	Rob_Dee	twopc	500000	50000000						5	0.012
2010-04-08	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-09	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-09	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-09	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-10	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-11	James Hintz	17_012210	250000	25000000						11	0.014
2010-04-11	James Hintz	17_012210	250000	25000000						11	0.014
2011-04-09	James Hintz	17_051310	250000	25000000						11	0.014
2013-04-03	BloodIce	Mjolnir	250000	25000000						150	0.186
2013-04-04	BloodIce	Mjolnir	250000	25000000						150	0.186
2013-04-04	BloodIce	Mjolnir	250000	25000000						90	0.112
2013-04-04	BloodIce	Mjolnir			9966065908771335003475470943081	102.975		1		1	-
2017-05-17	kkmrkkblmbrbk	c4.large	1000000	100000000						1372	6.823
2019-03-15	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-03-19	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-03-21	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-03-23	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-03-26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-03-28	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-03-30	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-04-01	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-04-03	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-04-06	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-04-08	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-04-10	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-04-12	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-04-16	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-04-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-04-23	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-04-26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-04-28	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-04-30	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000	694177295826160448071403167254080687	119.063	2	2		2	0.030
2019-05-03	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-05	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-08	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.045
2019-05-11	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-15	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-18	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-22	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-26	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-05-30	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-03	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-07	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-11	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-15	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-19	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-23	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-06-27	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.045
2019-07-06	Niels_Mache_Nextcloud		3000000	300000000						3	0.045
2019-07-20	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-07-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-07-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-07-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-03	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-21	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-08-26	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-08-28	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-08-31	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-02	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-09-05	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-09-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-10	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-13	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-18	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-21	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-09-23	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-09-28	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-01	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.045
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-12	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-14	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-17	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-19	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-25	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-27	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-10-30	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-01	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-06	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-09	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2019-11-12	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.045
2021-10-04	nordi	sweet16	3000000	427859251						800	13.59

Lucas-Lehmer results:
No L-L results for M14281

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

13938257

1805661079

148073604347344927871

9966065908771335003475470943081

1347A7048D9489EF

2017-09-21

Oliver Kruse

Manual testing

13938257

1805661079

148073604347344927871

9966065908771335003475470943081

1347A7048D9489EF

2017-10-02

kkmrkkblmbrbk

Manual testing

13938257

1805661079

148073604347344927871

9966065908771335003475470943081

1347A7048D9489__

2017-12-07

ATH

Manual testing

13938257

1805661079

148073604347344927871

9966065908771335003475470943081

1347A7048D9489__

2019-05-01

matzetoni

bobuba

13938257

1805661079

148073604347344927871

9966065908771335003475470943081

694177295826160448071403167254080687

147AB69B719AABB8

2019-05-02

Chang Chia-Tche

homura

13938257

1805661079

148073604347344927871

9966065908771335003475470943081

694177295826160448071403167254080687

147AB69B719AABB8

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

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=36.7 ~= 105-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2023-03-25T13:08:14+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