Numeros brillantes

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Números brillantes

Los números brillantes, definidos por Peter Wallrodt, son números con dos factores primos de la misma longitud (en notación decimal). Estos números se usan generalmente para propósitos criptográficos, y para hallar el rendimiento de los programas de factorización.

El problema consiste en continuar la tabla que se muestra abajo. Esta tabla contiene el número brillante más pequeño con una cantidad par de dígitos y el más grande con una cantidad impar de dígitos.

Es posible definir números n-brillantes como el producto de n números primos de la misma longitud.

Indice

Números 2-brillantes máximos y mínimos no triviales
Números 3-brillantes máximos y mínimos
Números 4-brillantes máximos y mínimos
Números 2-brillantes máximos y mínimos no triviales en base 2

**Números 2-brillantes máximos y mínimos no triviales**
Dígitos	Número	Factores primos	Descubridor
1	9	3	Jim Fougeron
1	9	3	Jim Fougeron
2	10	2
2	10	5
3	989	23
3	989	43
4	1003	17
4	1003	59
5	99973	257
5	99973	389
6	100013	103
6	100013	971
7	10⁷ - 189	1583
7	10⁷ - 189	6317
8	10⁷ + 43	2089
8	10⁷ + 43	4787
9	10⁹ - 137	25303
9	10⁹ - 137	39521
10	10⁹ + 81	26881
10	10⁹ + 81	37201
11	10¹¹ - 357	231571
11	10¹¹ - 357	431833
12	10¹¹ + 147	281683
12	10¹¹ + 147	355009
13	10¹³ - 77	1380163
13	10¹³ - 77	7245521
14	10¹³ + 73	1857929
14	10¹³ + 73	5382337
15	10¹⁵ - 261	18874013	Richard Heylen
15	10¹⁵ - 261	52982903	Richard Heylen
16	10¹⁵ + 3	14902357
16	10¹⁵ + 3	67103479
17	10¹⁷ - 297	150425719	Richard Heylen
17	10¹⁷ - 297	664779937	Richard Heylen
18	10¹⁷ + 831	158267567
18	10¹⁷ + 831	631841393
19	10¹⁹ - 533	1809444697	Richard Heylen
19	10¹⁹ - 533	5526557411	Richard Heylen
20	10¹⁹ + 49	1172005397
20	10¹⁹ + 49	8532383917
21	10²¹ - 353	21942092327	Richard Heylen
21	10²¹ - 353	45574505161	Richard Heylen
22	10²¹ + 987	10119972739
22	10²¹ + 987	98814495433
23	10²³ - 587	198168943561	Richard Heylen
23	10²³ - 587	504619937933	Richard Heylen
24	10²³ + 691	253850475563
24	10²³ + 691	393932687257
25	10²⁵ - 113	2701224339427	Richard Heylen
25	10²⁵ - 113	3702024986981	Richard Heylen
26	10²⁵ + 183	1634713216901
26	10²⁵ + 183	6117280937483
27	10²⁷ - 281	16816039284931	Richard Heylen
27	10²⁷ - 281	59467035195149	Richard Heylen
28	10²⁷ + 4153	10594044136579
28	10²⁷ + 4153	94392659413907
29	10²⁹ - 93	273350346504617	Richard Heylen
29	10²⁹ - 93	365830888011371	Richard Heylen
30	10²⁹ + 279	262922036885471
30	10²⁹ + 279	380340884258249
31	10³¹ - 389	1856935855186693	Richard Heylen
31	10³¹ - 389	5385215634707327	Richard Heylen
32	10³¹ + 667	1178160270652879
32	10³¹ + 667	8487809552819573
33	10³³ - 1083	27586826038690693	Richard Heylen
33	10³³ - 1083	36249186426792769	Richard Heylen
34	10³³ + 709	28567159477900867
34	10³³ + 709	35005230421091927
35	10³⁵ - 807	260929504743206393	Richard Heylen
35	10³⁵ - 807	383245275762949601	Richard Heylen
36	10³⁵ + 277	312315473725119131	Jim Fougeron
36	10³⁵ + 277	320189066546263567	Jim Fougeron
37	10³⁷ - 707	1124073940762336703	Richard Heylen
37	10³⁷ - 707	8896211928210070531	Richard Heylen
38	10³⁷ + 1687	2918984460772347259	Jim Fougeron
38	10³⁷ + 1687	3425849001386617493	Jim Fougeron
39	10³⁹ - 1071	22168728539128208483	Richard Heylen
39	10³⁹ - 1071	45108586098430581563	Richard Heylen
40	10³⁹ + 997	18288834983913311471	Jim Fougeron
40	10³⁹ + 997	54678168449744921707	Jim Fougeron
41	10⁴¹ - 3699	127062416457894753317	Richard Heylen
41	10⁴¹ - 3699	787014782086546036553	Richard Heylen
42	10⁴¹ + 1207	228728453883196320979	Jim Fougeron
42	10⁴¹ + 1207	437199650075309509133	Jim Fougeron
43	10⁴³ - 27	2551499368987998869591	Richard Heylen
43	10⁴³ - 27	3919264147796477703203	Richard Heylen
44	10⁴³ + 91	2094162205298508378983	Jim Fougeron
44	10⁴³ + 91	4775179293513497904877	Jim Fougeron
45	10⁴⁵ - 17	15380127434630196194863	Richard Heylen
45	10⁴⁵ - 17	65018967121714506226241	Richard Heylen
46	10⁴⁵ + 1411	20454925622447906868371	Jim Fougeron
46	10⁴⁵ + 1411	48887980257555528444241	Jim Fougeron
47	10⁴⁷ - 1677	279170318528058249521813	Richard Heylen
47	10⁴⁷ - 1677	358204269448327527799271	Richard Heylen
48	10⁴⁷ + 393	205522560092430172482139	Jim Fougeron
48	10⁴⁷ + 393	486564589089522586263787	Jim Fougeron
49	10⁴⁹ - 471	1943643268293290666134453	Richard Heylen
49	10⁴⁹ - 471	5144977045495071915161893	Richard Heylen
50	10⁴⁹ + 951	2647141521862657404330791	Jim Fougeron
50	10⁴⁹ + 951	3777659757670800343659761	Jim Fougeron
51	10⁵¹ - 579	29121661308190630398411623	Richard Heylen
51	10⁵¹ - 579	34338700303431672610407227	Richard Heylen
52	10⁵¹ + 9793	13953377225420926914498491	Jim Fougeron
52	10⁵¹ + 9793	71667237532871425027689523	Jim Fougeron
53	10⁵³ - 167	185862635189918295875711699	Richard Heylen
53	10⁵³ - 167	538031756075221497635484067	Richard Heylen
54	10⁵³ + 2217	140830196310821661891328463	Jim Fougeron
54	10⁵³ + 2217	710074988316378627095268359	Jim Fougeron
55	10⁵⁵ - 267	1049230952180343004616980607	Richard Heylen
55	10⁵⁵ - 267	9530790127015990538677972619	Richard Heylen
56	10⁵⁵ + 6229	1460201993355564860764167713	Jim Fougeron
56	10⁵⁵ + 6229	6848367585788496545968810933	Jim Fougeron
57	10⁵⁷ - 8349	24470570298372015475229439271	Jim Fougeron
57	10⁵⁷ - 8349	40865414569701641261618151781	Jim Fougeron
58	10⁵⁷ + 2317	21827649121989366053485370671	Jim Fougeron
58	10⁵⁷ + 2317	45813454046803015025118660227	Jim Fougeron
59	10⁵⁹ - 5973	100989110031147659340436549999	Jim Fougeron
59	10⁵⁹ - 5973	990205775347038981060013155973	Jim Fougeron
60	10⁵⁹ + 213	213916881789829278910570173437
60	10⁵⁹ + 213	467471286806848547076331371449
61	10⁶¹ - 69	1055217882882115232154201320731	Bouk de Water
61	10⁶¹ - 69	9476715815966853211400570143201	Bouk de Water
62	10⁶¹ + 399	1960582085021883125774065415291	Bouk de Water
62	10⁶¹ + 399	5100526051113225665789755534589	Bouk de Water
63	10⁶³ - 9	14499216344898896752959323769763	Bouk de Water
63	10⁶³ - 9	68969244696581083712684424134557	Bouk de Water
64	10⁶³ + 19	22350568628980377780095228766733	Jim Fougeron
64	10⁶³ + 19	44741590990368441481914582608543	Jim Fougeron
65	10⁶⁵ - 687	158997176633105910786856570509671	Bouk de Water
65	10⁶⁵ - 687	628941985748307323903185090439303	Bouk de Water
66	10⁶⁵ + 2317	286595216834133465028509515988163	Jim Fougeron
66	10⁶⁵ + 2317	348924176420832745825986935358959	Jim Fougeron
67	10⁶⁷ - 809	1250511065160951547577917550796961	Jim Fougeron
67	10⁶⁷ - 809	7996730519703889103364386584269431	Jim Fougeron
68	10⁶⁷ + 609	1678092783518480469813357050416541	Jim Fougeron
68	10⁶⁷ + 609	5959146060465656117945029500096149	Jim Fougeron
69	10⁶⁹ - 1241	10679904962845456862138386056396401	Phil Carmody
69	10⁶⁹ - 1241	93633792012093812114892571488571159	Phil Carmody
70	10⁶⁹ + 2607	24426597353643084809987417412256391	Jim Fougeron
70	10⁶⁹ + 2607	40938980797129151552564164844215577	Jim Fougeron
71	10⁷¹ - 7619	231008270216639494612708088690827091	Jim Fougeron
71	10⁷¹ - 7619	432884934838999601577138575168198191	Jim Fougeron
72	10⁷¹ + 11901	162435955060234923989750540378209139	Jim Fougeron
72	10⁷¹ + 11901	615627248061660606526348016196129359	Jim Fougeron
73	10⁷³ - 8297	2279546384325209074657090630001002097	Richard Heylen
73	10⁷³ - 8297	4386837692254372909233641841447115399	Richard Heylen
74	10⁷³ + 10563	1093872132886178625296967462523488383	Jim Fougeron
74	10⁷³ + 10563	9141836325617901427873699501869702461	Jim Fougeron
75	10⁷⁵ - 4209	11603482293180564213674824122706652977	Richard Heylen
75	10⁷⁵ - 4209	86181025207209215754156369211739413183	Richard Heylen
76	10⁷⁵ + 5473	11171602016259629892335959089815716691	Jim Fougeron (2 may 2002)
76	10⁷⁵ + 5473	89512676744531089226201976823759569403	Jim Fougeron (2 may 2002)
77	10⁷⁷ - 4851	266574540546930479652420365114117132441	Richard Heylen (10 may 2002)
77	10⁷⁷ - 4851	375129597128181069020562559344084771989	Richard Heylen (10 may 2002)
78	10⁷⁷ + 3	185554311496620532371770351611143673123	Jim Fougeron
78	10⁷⁷ + 3	538925768921415130739706333069119686561	Jim Fougeron
79	10⁷⁹ - 5667	1729776145369695994282075176946198769503	Richard Heylen
79	10⁷⁹ - 5667	5781094869858291625387593074971223276611	Richard Heylen
80	10⁷⁹ + 5923	1333322076518899001350381760807974795003	Richard Heylen (16 may 2002)
80	10⁷⁹ + 5923	7500063320115780212377802894180923803641	Richard Heylen (16 may 2002)
81	10⁸¹ - 4989	28090949127071263736011460619683106498869	Michael Bell
81	10⁸¹ - 4989	35598654765149940348772510523335003778519	Michael Bell
82	10⁸¹ + 17527	16185521526191837352841378940110747187933	Richard Heylen
82	10⁸¹ + 17527	61783613112606452271787097523839696139619	Richard Heylen
83	10⁸³ - 14333	199932327974298861069048863455316009796077	Richard Heylen (27 jun 2002)
83	10⁸³ - 14333	500169237327416700002311820952289282634671	Richard Heylen (27 jun 2002)
84	10⁸³ + 8569	132087033835831918079103641067858862243541	Richard Heylen (27 jun 2002)
84	10⁸³ + 8569	757076581220589828720159898116433821618709	Richard Heylen (27 jun 2002)
85	10⁸⁵ - 7007	1693200872034169587540836261917796700786223	Richard Heylen (8 jul 2002)
85	10⁸⁵ - 7007	5905973806868081574548312122783044390802991	Richard Heylen (8 jul 2002)
86	10⁸⁵ + 16701	3051275553674272224126253462719544495568863	Richard Heylen (27 sep 2002)
86	10⁸⁵ + 16701	3277317903313662333191415700136829929609827	Richard Heylen (27 sep 2002)
87	10⁸⁷ - 6113	16720583183841033646029730324154154355596829	Richard Heylen (11 oct 2002)
87	10⁸⁷ - 6113	59806526423457026799428621903555375545514603	Richard Heylen (11 oct 2002)
88	10⁸⁷ + 11989	25548073574973342022878007235853527655387529	Reto Keiser (25 jul 2002)
88	10⁸⁷ + 11989	39141894478478048759397262019204591690357741	Reto Keiser (25 jul 2002)
89	10⁸⁹ - 14547	171825942024805992446123879964620028962720089	Richard Heylen (24 nov 2002)
89	10⁸⁹ - 14547	581984296559615555233094293492402617340927477	Richard Heylen (24 nov 2002)
90	10⁸⁹ + 9757	125449117210655591881673183684137233747818249	Richard Heylen (24 nov 2002)
90	10⁸⁹ + 9757	797135940240048534567034950286701267149637493	Richard Heylen (24 nov 2002)
91	10⁹¹ - 35579	2978190131233156687766899939838042396357404141	David Cleaver (5 sep 2002)
91	10⁹¹ - 35579	3357743985223460380218440581090317089334569081	David Cleaver (5 sep 2002)
92	10⁹¹ + 6489	3030426176188825904708253480783779093519047793	David Cleaver (11 nov 2002)
92	10⁹¹ + 6489	3299865899579960543508682793462789222873063273	David Cleaver (11 nov 2002)
93	10⁹³ - 13643	13086519402050960470783685012210223925173521497	David Cleaver (9 dic 2002)
93	10⁹³ - 13643	76414512467178771426083642931523688230774568381	David Cleaver (9 dic 2002)
94	10⁹³ + 3489	29411667593005444701023975598270078264073129867	Jim Fougeron (9 dic 2002)
94	10⁹³ + 3489	34000112262856379670017139669568496330607787267	Jim Fougeron (9 dic 2002)
95	10⁹⁵ - 3681	111097491776794870937630002243840967616045495643	Richard Heylen (30 ene 2003)
95	10⁹⁵ - 3681	900110330131568068227760865309719427458876830733	Richard Heylen (30 ene 2003)
96	10⁹⁵ + 2899	136300932834042408394024592335302109536892634161	Jim Fougeron (12 dic 2002)
96	10⁹⁵ + 2899	733670694108588540814651977458574150528292043459	Jim Fougeron (12 dic 2002)
97	10⁹⁷ - 19163	1507302631098002948390959131169706059408828799543	David Cleaver (20 mar 2003)
97	10⁹⁷ - 19163	6634367773056592241515494527842465247176344374659	David Cleaver (20 mar 2003)
98	10⁹⁷ + 12577	1248259542695921544034940904194773338751647883781	Jim Fougeron (3 ene 2003)
98	10⁹⁷ + 12577	8011154457832187771253603613895408568341998334317	Jim Fougeron (3 ene 2003)
99	10⁹⁹ - 2783	31084801612134411476333699496627802172660847517087	David Cleaver (13 dic 2002)
99	10⁹⁹ - 2783	32170062156987845422435581553308407138632546972991	David Cleaver (13 dic 2002)
100	10⁹⁹ + 4011	23156485057650669192768497163340558192130875875893	David Cleaver (20 dic 2002)
100	10⁹⁹ + 4011	43184446927518910400647566770334520938655251359327	David Cleaver (20 dic 2002)
101	10¹⁰¹ - 56993	117824543400831857004264281890859168944172987388481	David Cleaver (4 mar 2003)
101	10¹⁰¹ - 56993	848719605556256173460898892513108240280912733932447	David Cleaver (4 mar 2003)
102	10¹⁰¹ + 3231	227019196535950614963176497989255069045234236491673	Richard Heylen (13 jul 2003)
102	10¹⁰¹ + 3231	440491383662192037893868941350132265860839934720247	Richard Heylen (13 jul 2003)
103	10¹⁰³ - 2417	2388684044013249161833428010656139781947511337567461	David Cleaver (20 jul 2003)
103	10¹⁰³ - 2417	4186405491786561972002257851552363665292291130223203	David Cleaver (20 jul 2003)
104	10¹⁰³ + 17389	2178850329744203343440104133177891981618919402435883	David Cleaver (17 ago 2003)
104	10¹⁰³ + 17389	4589576375892693047888073495994066512714871682387783	David Cleaver (17 ago 2003)
105	10¹⁰⁵ - 30179	20072845108389786097528973616362100626048357754871711	Richard Heylen (14 oct 2003)
105	10¹⁰⁵ - 30179	49818548123107522887110525377542084788096962615971011	Richard Heylen (14 oct 2003)
106	10¹⁰⁵ + 4293	12842269977506686435684442645814821681335988332440829	Richard Heylen (1 ago 2003)
106	10¹⁰⁵ + 4293	77867853716788858218366878517755270539950026013843817	Richard Heylen (1 ago 2003)
107	10¹⁰⁷ - 569	298108931508935388275225546217432865020464146509030899	Richard Heylen (22 oct 2003)
107	10¹⁰⁷ - 569	335447849528797640933380616577564706751493530526472669	Richard Heylen (22 oct 2003)
108	10¹⁰⁷ + 6969	200017903493958497496269825834649922840822467385473869	Richard Heylen (30 oct 2003)
108	10¹⁰⁷ + 6969	499955245271433818753431743345545907675226421199679901	Richard Heylen (30 oct 2003)
109	10¹⁰⁹ - 10617	2939293471451715027656817574156459818963532929889785991	Richard Heylen (30 nov 2003)
109	10¹⁰⁹ - 10617	3402178141490923281380298543164480324704096301595136513	Richard Heylen (30 nov 2003)
110	10¹⁰⁹ + 19041	2762291535441394586840378227581982108373140647210683969	David Cleaver (16 nov 2003)
110	10¹⁰⁹ + 19041	3620182689515453682000526808729199471973438435837408289	David Cleaver (16 nov 2003)
111	10¹¹¹ - 11957	14118203979842718112107179085913584270402578821772762747	Richard Heylen (5 abr 2004)
111	10¹¹¹ - 11957	70830539169695461569685870350892702678351054824192755569	Richard Heylen (5 abr 2004)
112	10¹¹¹ + 57339	16276909230503536141393381740491200391483078776043167501	Sander Hoogendoorn (15 mar 2006)
112	10¹¹¹ + 57339	61436725230731313013378040084827321449103017270012524839	Sander Hoogendoorn (15 mar 2006)
113	10¹¹³ - 91227	135483731348216310599104139961914909156900674425643544869	Sander Hoogendoorn (20 abr 2006)
113	10¹¹³ - 91227	738095998721668909879514364987164877946232346531808934017	Sander Hoogendoorn (20 abr 2006)
114	10¹¹³ + 29359	129956782241538606843279942501870615823682988388592729389	David Cleaver (27 mar 2007)
114	10¹¹³ + 29359	769486580655246475123803852893690968086716734490830614731	David Cleaver (27 mar 2007)
115	10¹¹⁵ - 1769	1150412009677946969526346072331760233354867799371253396127	David Cleaver (1 abr 2007)
115	10¹¹⁵ - 1769	8692537904571648356378342160363552634406563631760612220553	David Cleaver (1 abr 2007)
116	10¹¹⁵ + 12741	1659340911132774307356923305106837591426034334709864681011	Sander Hoogendoorn (28 abr 2006)
116	10¹¹⁵ + 12741	6026489151752033839345332361847936212205931651365703227431	Sander Hoogendoorn (28 abr 2006)
148	10¹⁴⁷ + 19	11210754325987903848222358333498946062147584250342963305961590952868977237	Andreas Höglund (29 jul 2006)
148	10¹⁴⁷ + 19	89200063699717094086741570686240243731188867201010229921060666406453209287	Andreas Höglund (29 jul 2006)
150	10¹⁴⁹ + 21553	196175124573517092034922493422470908957491913295260473203518969764669282857	Paul Leyland (6 jul 2006)
150	10¹⁴⁹ + 21553	509748624946200879944668835201017220741864841301635474800405920115982269129	Paul Leyland (6 jul 2006)

**Números 3-brillantes máximos y mínimos**
Dígitos	Mínimo	Factores primos	Descubridor	Máximo	Factores primos	Descubridor
1	8	2 2 2	Trivial	8	2 2 2	Richard Heylen
2	12	2 2 3		98	2 7 7	Richard Heylen
3	105	3 5 7		343	7 7 7	Trivial
4	1331	11 11 11	Trivial	9971	13 13 59	Richard Heylen
5	10013	17 19 31		99937	37 37 73	Richard Heylen
6	100181	17 71 83		912673	97 97 97	Trivial
7	1030301	101 101 101	Trivial	10⁷ - 293	101 181 547	Richard Heylen
8	10⁷ + 127	167 233 257	Sander Hoogendoorn	10⁸ - 333	223 509 881	Richard Heylen
9	10⁸ + 727	331 397 761	Sander Hoogendoorn	991026973	997 997 997	Trivial
10	1009³	1009 1009 1009	Trivial	10¹⁰ - 533	1117 1997 4483	Richard Heylen
11	10¹⁰ + 2797	1201 1367 6091	Richard Heylen	10¹¹ - 993	3847 4481 5801	Richard Heylen
12	10¹¹ + 757	2879 4643 7481	Richard Heylen	9973³	9973 9973 9973	Trivial
13	10007³	10007 10007 10007	Trivial	10¹³ - 5229	10589 22679 41641	Richard Heylen
14	10¹³ + 493	14779 22397 30211	Richard Heylen	10¹⁴ - 5883	29333 53693 63493	Richard Heylen
15	10¹⁴ + 5643	36887 48679 55691	Richard Heylen	99991³	99991 99991 99991	Trivial
16	100003³	100003 100003 100003	Trivial	10¹⁶ - 2903	146383 182981 373339	Richard Heylen
17	10¹⁶ + 1251	165833 205703 293149	Richard Heylen	10¹⁷ - 7977	251879 616999 643463	Richard Heylen
18	10¹⁷ + 649	211801 589189 801341	Richard Heylen	999983³	999983 999983 999983	Trivial
19	(10⁶ + 3)³	1000003 1000003 1000003	Trivial	10¹⁹ - 5417	1750769 1777931 3212597	Richard Heylen
20	10¹⁹ + 2149	1633561 2124037 2882057	Richard Heylen	10²⁰ - 11297	2994503 5625617 5936153	Richard Heylen
21	10²⁰ + 6043	1418159 8250113 8547029	Richard Heylen	(10⁷ - 9)³	9999991 9999991 9999991	Trivial
22	(10⁷ + 19)³	10000019 10000019 10000019	Trivial	10²² - 773	10186663 19042489 51551861	Richard Heylen
23	10²² + 2427	10073153 31104971 31915729	Richard Heylen	10²³ - 489	18775423 57543443 92558099	Richard Heylen
24	10²³ + 1509	21110813 49732283 95248171	Richard Heylen	(10⁸ - 11)³	99999989 99999989 99999989	Trivial
25	(10⁸ + 7)³	100000007 100000007 100000007	Trivial	10²⁵ - 3899	125786989 158352281 502041889	Richard Heylen
26	10²⁵ + 16189	106371977 114768809 819122573	Richard Heylen	10²⁶ - 16359	180617837 594451513 931371461	Richard Heylen
27	10²⁶ + 5751	236902847 554251279 761593127	Richard Heylen	(10⁹ - 63)³	999999937 999999937 999999937	Trivial
28	(10⁹ + 7)³	1000000007 1000000007 1000000007	Trivial	10²⁸ - 13067	1292215579 1624184473 4764635399	Richard Heylen
29	10²⁸ + 14707	1005841013 2737363219 3631936381	Richard Heylen	10²⁹ - 16409	2228847419 5521017059 8126444471	Richard Heylen
30	10²⁹ + 29013	1691348917 6316788229 9359884141	Richard Heylen	(10¹⁰ - 33)³	9999999967 9999999967 9999999967	Trivial
31	(10¹⁰ + 19)³	10000000019 10000000019 10000000019	Trivial	10³¹ - 64611	13689527419 19896130049 36714949319	Richard Heylen
32	10³¹ + 5893	11198428391 13492646957 66182895839	Richard Heylen	10³² - 21003	41994700453 42965141327 55422902687	Richard Heylen (26 abr 2002)
33	10³² + 1927	26464641997 40362051277 93618299183	Richard Heylen	(10¹¹ - 23)³	99999999977 99999999977 99999999977	Trivial
34	(10¹¹ + 3)³	100000000003 100000000003 100000000003	Trivial	10³⁴ - 14933	114850721137 118686379657 733610250563	Richard Heylen (26 abr 2002)
35	10³⁴ + 52737	119495634017 224778984407 372299332423	Richard Heylen	10³⁵ - 25911	273483275773 445466326247 820832127419	Richard Heylen (26 abr 2002)
36	10³⁵ + 4399	302832767711 345905509051 954640061059	Richard Heylen	(10¹² - 11)³	999999999989 999999999989 999999999989	Trivial
37	(10¹² + 39)³	1000000000039 1000000000039 1000000000039	Trivial	10³⁷ - 28839	1262313101783 1946468711927 4069916348521	Richard Heylen (26 abr 2002)
38	10³⁷ + 123819	1236706881791 2374655713867 3405121160927	Jim Fougeron	10³⁸ - 149759	3459465859009 5328480059843 5424848400043	Richard Heylen
39	10³⁸ + 158041	3586186059383 4367940094321 6383965165087	Jim Fougeron	(10¹³ - 29)³	9999999999971 9999999999971 9999999999971	Trivial
40	(10¹³ + 37)³	10000000000037 10000000000037 10000000000037	Trivial	10⁴⁰ - 213617	17363198401447 20739646816249 27769554715361	Richard Heylen
41	10⁴⁰ + 130957	12814854302599 14964561505277 52146159843559	Richard Heylen	10⁴¹ - 6567	34903487411119 42063334550063 68112603333689	Richard Heylen
42	10⁴¹ + 17353	24407650660903 55069088040739 74398835289509	Richard Heylen	(10¹⁴ - 27)³	99999999999973 99999999999973 99999999999973	Trivial
43	(10¹⁴ + 31)³	100000000000031 100000000000031 100000000000031	Trivial	10⁴³ - 146909	172300505289967 211820845471373 273996333782401	Jim Fougeron
44	10⁴³ + 59587	101663821593379 154251196872133 637683274853741	Donovan Johnson (17 sep 2007)	10⁴⁴ - 196587	204797993723737 529220463976397 922651459305617	Jim Fougeron
45	10⁴⁴ + 65863	183984656831567 555439604761381 978546684274069	Jim Fougeron	(10¹⁵ - 11)³	999999999999989 999999999999989 999999999999989	Trivial
46	(10¹⁵ + 37)³	1000000000000037 1000000000000037 1000000000000037	Trivial	10⁴⁶ - 65553	1257239303812309 1514462531713763 5251985486925041	Jim Fougeron
47	10⁴⁶ + 50527	1379143216396571 2130751443448703 3402967810987379	Jim Fougeron	10⁴⁷ - 62673	2249340625367531 5634982736187193 7889549094998069	Jim Fougeron
48	10⁴⁷ + 88291	2772015045385711 4080087583803271 8841682815196811	Jim Fougeron	(10¹⁶ - 63)³	9999999999999937 9999999999999937 9999999999999937	Trivial
49	(10¹⁶ + 61)³	10000000000000061 10000000000000061 10000000000000061	Trivial	10⁴⁹ - 192557	10584419300262271 27959929042948027 33790677470564279	Jim Fougeron
50	10⁴⁹ + 31741	14778664291304861 25683013132372291 26346252045255691	Jim Fougeron	10⁵⁰ - 229457	18946951128091531 63046191097099543 83714716546569371	Jim Fougeron
51	10⁵⁰ + 124891	21223204371030971 63048999783056603 74732729167701107	Jim Fougeron	(10¹⁷ - 3)³	99999999999999997 99999999999999997 99999999999999997	Trivial
52	(10¹⁷ + 3)³	100000000000000003 100000000000000003 100000000000000003	Trivial	10⁵² - 176477	133998667582700839 174686342410900561 427209172135519637	Richard Heylen (10 may 2002)
53	10⁵² + 136711	127164238960370737 259430702647849189 303119329497323627	Richard Heylen (10 may 2002)	10⁵³ - 288257	326171326139830487 479381522599043591 639547683418675679	Richard Heylen (10 may 2002)
54	10⁵³ + 17473	124579059080641657 833903327864200817 962585347616078617	Richard Heylen (10 may 2002)	(10¹⁸ - 11)³	999999999999999989 999999999999999989 999999999999999989	Trivial
55	(10¹⁸ + 3)³	1000000000000000003 1000000000000000003 1000000000000000003	Trivial	10⁵⁵ - 219503	1575853845858412391 1655415652335968641 3833337050952127687	Richard Heylen (14 may 2002)
56	10⁵⁵ + 32089	1267227113342116519 1843431668851243501 4280736536975381531	Richard Heylen (14 may 2002)	10⁵⁶ - 40667	2395810946112780733 4466726666846584747 9344543235276726683	Richard Heylen
57	10⁵⁶ + 492649	2514380642884427987 4342954421922749933 9157642889778573119	Richard Heylen (14 may 2002)	(10¹⁹ - 39)³	9999999999999999961 9999999999999999961 9999999999999999961	Trivial
58	(10¹⁹ + 51)³	10000000000000000051 10000000000000000051 10000000000000000051	Trivial	10⁵⁸ - 267239	11632532594322798479 26618303856556487219 32295747692831078861	Richard Heylen (22 may 2002)
59	10⁵⁸ + 108081	13828075410413032133 17980427028526107161 40219647399720069637	Richard Heylen (22 may 2002)	10⁵⁹ - 76619	28256759918246059307 38549172961130847991 91804204822980213913	Richard Heylen (22 may 2002)
60	10⁵⁹ + 76107	25996429356478022461 54578705970898911931 70479540545693881477	Richard Heylen (22 may 2002)	(10²⁰ - 11)³	99999999999999999989 99999999999999999989 99999999999999999989	Trivial
61	(10²⁰ + 39)³	100000000000000000039 100000000000000000039 100000000000000000039	Trivial	10⁶¹ - 8399	140881594246452086939 238903948375968285643 297113520291914005513	Richard Heylen (28 jun 2002)
62	10⁶¹ + 188527	198215253418203418427 212063210537599457801 237901727598652088501	Donovan Johnson (27 sep 2007)	10⁶² - 28967	126765938565324144143 870031810053723383309 906697236767450667059	Richard Heylen (27 jun 2002)
63	10⁶² + 1058637	295938758296861970419 448144368785742725801 754015388102253507623	Richard Heylen (27 jun 2002)	(10²⁰ - 101)³	999999999999999999899 999999999999999999899 999999999999999999899	Trivial
64	(10²¹ + 117)³	1000000000000000000117 1000000000000000000117 1000000000000000000117	Trivial	10⁶⁴ - 57651	1061035345578788338541 1391023341645011752009 6775412341858197416921	Richard Heylen (27 jun 2002)
65	10⁶⁴ + 85803	1714618450864782471611 2329234269479119539521 2503913582603801962513	Richard Heylen (27 jun 2002)	10⁶⁵ - 1729751	3677679547530663653161 4254537295896375206353 6391073032088863400753	Richard Heylen (30 ene 2003)
66	10⁶⁵ + 149259	1835808612551245318829 5728537695516908168719 9508868068476315618809	Richard Heylen (30 ene 2003)	(10²² - 27)³	9999999999999999999973 9999999999999999999973 9999999999999999999973	Trivial
67	(10²² + 9)³	10000000000000000000009 10000000000000000000009 10000000000000000000009	Trivial	10⁶⁷ - 901821	10101615893692369271767 17531974986675607157429 56464866654909501084353	Richard Heylen (18 may 2003)
68	10⁶⁷ + 534037	11589548025741092487547 18965422792905017360051 45495764971886030329621	Richard Heylen (16 mar 2003)	10⁶⁸ - 26039	12074017005366544874783 87236000943598050131963 94940708489892063116309	Richard Heylen (5 ene 2003)
69	10⁶⁸ + 192507	17663201672959682401741 68347532202803380194037 82833828425856284929771	Richard Heylen (21 mar 2003)	(10²³ - 23)³	99999999999999999999977 99999999999999999999977 99999999999999999999977	Trivial
70	(10²³ + 117)³	100000000000000000000117 100000000000000000000117 100000000000000000000117	Trivial	10⁷⁰ - 96509	168408859236958014948709 240549351041680305101809 246848718161192945885111	Richard Heylen (17 mar 2003)
71	10⁷⁰ + 438499	125932443710597528749973 219951245631973461246409 361023891574669178861407	Richard Heylen (14 oct 2003)	10⁷¹ - 171	350919411515989914399433 456095644213453949493941 624793759241398759715993	Richard Heylen
72	10⁷¹ + 283093	223870743276389461972199 635533664645795858603047 702852345491672800196581	Richard Heylen (14 oct 2003)	(10²⁴ - 257)³	999999999999999999999743 999999999999999999999743 999999999999999999999743	Trivial
73	(10²⁴ + 7)³	1000000000000000000000007 1000000000000000000000007 1000000000000000000000007	Trivial	10⁷³ - 501113	1084484584660005964247077 1546319684139286596653819 5963171949495925649715649	Donovan Johnson (6 oct 2007)
74	10⁷³ + 111441	1560742180771083281388349 1793577197271133261268279 3572306866130364500807171	Richard Heylen (5 abr 2004)	10⁷⁴ - 23523	3146025203611921936230217 4492220097138647112441799 7075819992450556090832419	Richard Heylen (5 abr 2004)
75	10⁷⁴ + 15061	4283452594120204339048033 4505070643133323591195913 5182083775943267656500109	Richard Heylen (19 feb 2004)	(10²⁵ - 123)³	9999999999999999999999877 9999999999999999999999877 9999999999999999999999877	Trivial
76	(10²⁵ + 13)³	10000000000000000000000013 10000000000000000000000013 10000000000000000000000013	Trivial	10⁷⁶ - 291249	15633890400259856213478307 23821644499003257798605369 26851045330260867259821197	Donovan Johnson (9 oct 2007)
77	10⁷⁶ + 65311	10609639225498094253225569 11880458198152686560316113 79335249741846477883350863	Donovan Johnson (6 oct 2007)	10⁷⁷ - 910473	36506267167202217741394931 51431759388815828667418817 53260003564945654181942701	Predrag Minovic (8 abr 2007)
78	10⁷⁷ + 395353	26022738012542679467808233 50789395724565737472464827 75661328886633682119158083	Donovan Johnson (9 oct 2007)
79	(10²⁶ + 67)³	100000000000000000000000067 100000000000000000000000067 100000000000000000000000067	Trivial	10⁷⁹ - 392931	143292513957372727386413437 264088185130417093421531701 264257624023096159956859837	Donovan Johnson (16 dec 2007)

**Números 4-brillantes máximos y mínimos**
Dígitos	Mínimo	Factores primos	Descubridor	Máximo	Factores primos	Descubridor
2	16	2 2 2 2	Bouk de Water	90	2 3 3 5	Bouk de Water
3	100	2 2 5 5	Bouk de Water	875	5 5 5 7	Bouk de Water
4	1029	3 7 7 7	Bouk de Water	2401	7 7 7 7	Trivial
5	14641	11 11 11 11	Trivial	99671	11 13 17 41	Bouk de Water
6	100529	11 13 19 37	Bouk de Water	999973	13 13 61 97	Bouk de Water
7	10⁶ + 109	11 23 59 67	Bouk de Water	10⁷ - 8709	17 73 83 97	Bouk de Water
8	10⁷ + 5647	19 61 89 97	Richard Heylen (16 may 2002)	97⁴	97 97 97 97	Trivial
9	101⁴	101 101 101 101	Trivial	10⁹ - 2717	107 109 179 479	Bouk de Water
10	10⁹ + 2847	107 167 191 293	Bouk de Water	10¹⁰ - 1671	163 241 277 919	Bouk de Water
11	10¹⁰ + 861	103 157 653 947	Bouk de Water	10¹¹ - 2289	311 397 829 977	Richard Heylen (16 may 2002)
12	10¹¹ + 24219	389 401 643 997	Bouk de Water	997⁴	997 997 997 997	Trivial
13	1009⁴	1009 1009 1009 1009	Trivial	10¹³ - 191	1051 1117 2063 4129	Bouk de Water
14	10¹³ + 54129	1321 1423 2087 2549	Bouk de Water	10¹⁴ - 11021	2161 2297 3019 6673	Bouk de Water
15	10¹⁴ + 9729	1033 3109 5479 5683	Bouk de Water	10¹⁵ - 8459	2939 4957 7907 8681	Bouk de Water
16	10¹⁵ + 11799	3499 5741 6133 8117	Bouk de Water	9973⁴	9973 9973 9973 9973	Trivial
17	10007⁴	10007 10007 10007 10007	Trivial	10¹⁷ - 194271	13337 14537 17401 29641	Bouk de Water
18	10¹⁷ + 35241	11717 13469 18047 35111	Richard Heylen (16 may 2002)	10¹⁸ - 31247	15773 19301 40697 80713	Richard Heylen (16 May 2002)
19	10¹⁸ + 12861	20327 26849 27431 66797	Richard Heylen (16 may 2002)	10¹⁹ - 165507	31891 38453 83617 97523	Richard Heylen (16 may 2002)
20	10¹⁹ + 80101	27103 63317 68213 85427	Richard Heylen (16 may 2002)	99991⁴	99991 99991 99991 99991	Trivial
21	100003⁴	100003 100003 100003 100003	Trivial	10²¹ - 40167	107453 167747 179497 309079	Richard Heylen (16 may 2002)
22	10²¹ + 200239	100057 123923 164429 490481	Richard Heylen (16 may 2002)	10²² - 43197	171761 296827 439493 446293	Richard Heylen (16 may 2002)
23	10²² + 146433	140477 272759 309157 844183	Richard Heylen (16 may 2002)	10²³ - 121227	393629 519031 625909 782003	Richard Heylen (16 may 2002)
24	10²³ + 22597	304553 460841 765503 930763	Richard Heylen (16 may 2002)	999983⁴	999983 999983 999983 999983	Trivial
25	(10⁶ + 3)⁴	1000003 1000003 1000003 1000003	Trivial	10²⁵ - 225371	1090409 1356721 1794679 3766459	Richard Heylen (16 may 2002)
26	10²⁵ + 719407	1178231 1184987 1761671 4065661	Richard Heylen (16 may 2002)	10²⁶ - 12227	1494659 2763377 4873753 4967687	Richard Heylen (16 may 2002)
27	10²⁶ + 44047	1157759 2399869 4320469 8330353	Richard Heylen (16 may 2002)	10²⁷ - 181239	4668211 5065199 5361887 7887427	Richard Heylen (22 may 2002)
28	10²⁷ + 358173	2410043 4761727 9033361 9646313	Richard Heylen (22 may 2002)	(10⁷ - 9)⁴	9999991 9999991 9999991 9999991	Trivial
29	(10⁷ + 19)⁴	10000019 10000019 10000019 10000019	Trivial	10²⁹ - 121587	10211363 14281931 22793899 30082279	Sander Hoogendoorn
30	10²⁹ + 784329	13503449 15690811 21475043 21977377	Jim Fougeron	10³⁰ - 225131	14671121 16358479 60823691 68504801	Sander Hoogendoorn
31	10³⁰ + 46197	24847783 26380859 37443787 40742123	Jim Fougeron	10³¹ - 64409	43520599 50243803 63662927 71834989	Sander Hoogendoorn
32	10³¹ + 120531	40738811 52961729 56976001 81346249	Jim Fougeron	(10⁸ - 11)⁴	99999989 99999989 99999989 99999989	Trivial
33	(10⁸ + 7)⁴	100000007 100000007 100000007 100000007	Trivial	10³³ - 2981361	138811943 150388417 172824791 277174159	Richard Heylen (9 ago 2002)
34	10³³ + 6379	121022911 132294061 169058819 369448771	Jim Fougeron	10³⁴ - 291003	160575161 169865251 543834983 674139769	Richard Heylen (9 ago 2002)
35	10³⁴ + 1167691	117930893 237943709 381975661 932958863	Jim Fougeron	10³⁵ - 7133483	249412637 577688777 800184277 867356429	Richard Heylen (9 ago 2002)
36	10³⁵ + 1553517	229833959 596374529 837572501 871052447	Jim Fougeron	(10⁹ - 63)⁴	999999937 999999937 999999937 999999937	Trivial
37	(10⁹ + 7)⁴	1000000007 1000000007 1000000007 1000000007	Trivial	10³⁷ - 3392961	1024919407 1205624261 2704285817 2992579621	Jim Fougeron
38	10³⁷ + 73269	1015004657 2113986011 2124717653 2193454499	Jim Fougeron	10³⁸ - 1209213	1277941309 3496358689 4329118921 5169798247	Jim Fougeron
39	10³⁸ + 1505619	2535959857 3100290539 3280439369 3877244737	Jim Fougeron	10³⁹ - 716501	2188752617 6832015219 7332337547 9120361379	Jim Fougeron
40	10³⁹ + 5560879	2806287299 5684681111 7330103057 8551684723	Jim Fougeron	(10¹⁰ - 33)⁴	9999999967 9999999967 9999999967 9999999967	Trivial
41	(10¹⁰ + 19)⁴	10000000019 10000000019 10000000019 10000000019	Trivial	10⁴¹ - 1752149	11665636553 12020765051 12486083933 57112766749	Jim Fougeron
42	10⁴¹ + 270387	10057723799 14695606843 16439060371 41156248421	Jim Fougeron	10⁴² - 1968921	16387356763 29844439783 35069159969 58304529779	Jim Fougeron
43	10⁴² + 190281	12904941277 28529199667 51682064947 52555058197	Jim Fougeron	10⁴³ - 812357	32266433293 66076452031 68130819217 68842829513	Jim Fougeron
44	10⁴³ + 186541	36717661187 40254606487 71613321583 94474714183	Jim Fougeron	(10¹¹ - 23)⁴	99999999977 99999999977 99999999977 99999999977	Trivial
45	(10¹¹ + 3)⁴	100000000003 100000000003 100000000003 100000000003	Trivial	10⁴⁵ - 1021013	111193045207 162288480071 170369552917 325269018463	Phil Carmody (26 oct 2003)
46	10⁴⁵ + 5945727	109637540401 130495801231 157056159707 445029913331	Richard Heylen (11 jul 2002)	10⁴⁶ - 550623	114257545709 301659452561 369064621643 786132506111	Phil Carmody (26 oct 2003)
47	10⁴⁶ + 3940503	118764538069 214272532333 513125859067 765813137317	Richard Heylen (19 jul 2002)	10⁴⁷ - 12394547	258602566111 537704923703 784384962709 916840728049	Phil Carmody (27 oct 2003)
48	10⁴⁷ + 6265441	255256467691 678739441577 705264620759 818404596557	Donovan Johnson (30 ago 2007)	(10¹² - 11)⁴	999999999989 999999999989 999999999989 999999999989	Trivial
49	(10¹² + 39)⁴	1000000000039 1000000000039 1000000000039 1000000000039	Trivial	10⁴⁹ - 1328811	1123363694533 1132900299593 1619376154261 4852216658021	Predrag Minovic (25 abr 2006)
50	10⁴⁹ + 679663	1159788556469 1175245695677 1976861376901 3711216539651	Richard Heylen (2 ago 2002)	10⁵⁰ - 1827771	1131830822071 2299071133453 4626382993013 8306622844691	Andreas Höglund (22 ago 2006)
51	10⁵⁰ + 874531	2031459510449 2646219932437 3821581909133 4867687850339	Sander Hoogendoorn (17 nov 2003)	10⁵¹ - 2839931	2610618693979 4981318597973 8607852782717 8933412874271	Andreas Höglund (16 sep 2006)
52	10⁵¹ + 24031807	3586045996369 5155570211641 6706659821857 8064940359719	Andreas Höglund (16 sep 2006)	(10¹³ - 29)⁴	9999999999971 9999999999971 9999999999971 9999999999971	Trivial
53	(10¹³ + 37)⁴	10000000000037 10000000000037 10000000000037 10000000000037	Trivial	10⁵³ - 853581	13801633011217 15102457237171 15359336773961 31235570830697	Richard Heylen
54	10⁵³ + 2626077	12517623121403 12777073989481 16667362777847 37512830115337	Donovan Johnson (30 ago 2007)	10⁵⁴ - 5526581	15039932275681 28441324348441 44484945266719 52552241384381	Donovan Johnson (26 sep 2007)
55	10⁵⁴ + 1293679	15739418315123 31371181661341 38173288431427 53054334421939	Donovan Johnson (7 sep 2007)	10⁵⁵ - 1372949	19993325988847 73485361492133 80952155039507 84078644846843	Donovan Johnson (26 sep 2007)
56	10⁵⁵ + 26082931	31465199992697 50998056344693 66759528591367 93347484189833	Donovan Johnson (3 oct 2007)	(10¹⁴ - 27)⁴	99999999999973 99999999999973 99999999999973 99999999999973	Trivial
57	(10¹⁴ + 31)⁴	100000000000031 100000000000031 100000000000031 100000000000031	Trivial	10⁵⁷ - 4541	103086207782083 152179523379973 211276757911589 301711242208009	Richard Heylen (2 jun 2003)
58	10⁵⁷ + 1811253	117856492897181 131917327092977 204532887090121 314471646669889	Richard Heylen (3 sep 2002)	10⁵⁸ - 4187751	143428321659551 236119351144679 523981514063681 563530643461601	Donovan Johnson (26 sep 2007)
59	10⁵⁸ + 5803147	122262486564571 258372872730919 555905946893789 569453860946227	Donovan Johnson (12 sep 2007)	10⁵⁹ - 14655741	313736165207561 536135329528819 672035000546687 884645142291223	Donovan Johnson (26 sep 2007)
60	10⁵⁹ + 36711589	266542160903959 622245970511791 630099845622983 956891329848907	Donovan Johnson (3 oct 2007)	(10¹⁵ - 11)⁴	999999999999989 999999999999989 999999999999989 999999999999989	Trivial
61	(10¹⁵ + 37)⁴	1000000000000037 1000000000000037 1000000000000037 1000000000000037	Trivial	10⁶¹ - 22336827	1156112937602863 1821568051966979 1985228621423119 2391904358614871	Donovan Johnson (30 sep 2007)
62	10⁶¹ + 470193	1456513870035241 1731482834726159 1752389428378763 2262749930928469	Donovan Johnson (12 sep 2007)	10⁶² - 4626803	1622599674057919 2172008813516923 3073884742899533 9230802373690957	Richard Heylen (17 sep 2003)
63	10⁶² + 5111959	2279143986837019 2779912264720531 3576658593158251 4412855031576581	Donovan Johnson (12 sep 2007)	10⁶³ - 34575809	3237564338664067 3415229830176679 9445468489873021 9574986131281247	Donovan Johnson (9 oct 2007)
64	10⁶³ + 18799597	2659618573195897 5339403019173071 7570134814101641 9302171161690691	Donovan Johnson (17 sep 2007)	(10¹⁶ - 63)⁴	9999999999999937 9999999999999937 9999999999999937 9999999999999937	Trivial
65	(10¹⁶ + 61)⁴	10000000000000061 10000000000000061 10000000000000061 10000000000000061	Trivial	10⁶⁵ - 11058639	11991999226304927 14191385939851301 17850368215222619 32918225659149497	Donovan Johnson (3 oct 2007)
66	10⁶⁵ + 16528921	11582582156494837 16857241544984641 19535307537073043 26217293034303991	Donovan Johnson (14 sep 2007)	10⁶⁶ - 1194869	16689608733528161 18877791141985067 35471007677518727 89480652326297719	Donovan Johnson (30 sep 2007)
67	10⁶⁶ + 1037911	21291651498132551 27133413015756133 33930229792704437 51015180136202441	Donovan Johnson (14 sep 2007)
68	10⁶⁷ + 3136153	22337954099825591 75478603724282501 76572821197688237 77456541233638159	Donovan Johnson (17 sep 2007)	(10¹⁷ - 3)⁴	99999999999999997 99999999999999997 99999999999999997 99999999999999997	Trivial
69	(10¹⁷ + 3)⁴	100000000000000003 100000000000000003 100000000000000003 100000000000000003	Trivial
70	10⁶⁹ + 2495233	111053578017928633 112251513276295871 150800642421161699 531951512758103069	Donovan Johnson (14 sep 2007)
71	10⁷⁰ + 15754711	145813808529168361 205631780744229349 389667325576323679 855888358348768781	Donovan Johnson (17 sep 2007)
75	10⁷⁴ + 5773243	1375956653530253917 2772933156399582559 2963465354433379559 8844147812502586159	Donovan Johnson (26 sep 2007)

Si usted conoce un número que deba ir en estas tablas o tiene algún comentario, por favor llene el formulario.

Actualizado el 4 de febrero de 2008.