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brilliant numbers
A semiprime  $p\cdot q$  for which  $p$  and  $q$  have the same number of digits is called brilliant number.

The smallest 3 × 3 magic square whose entries are brilliant numbers with no common factors is

181 ⋅ 337149 ⋅ 82123 ⋅ 41 60997 122329 943
37 ⋅ 37239 ⋅ 257331 ⋅ 367 =  1369 61423 121477
139 ⋅ 87711 ⋅ 47127 ⋅ 487 121903 517 61849

The first brilliant numbers are 4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 341, 361, 377 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of brilliant numbers

A graph displaying how many brilliant numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of brilliant numbers
Useful links OEIS, sequence A078972
Dario Alpern, Brilliant Numbers
Brilliant numbers can also be... (you may click on names or numbers and on + to get more values)

aban 10 14 15 + 999000973 alternating 10 14 21 + 989898769 amenable 21 25 49 + 999999421 apocalyptic 247 361 529 + 29999 arithmetic 14 15 21 + 9999811 astonishing 15 automorphic 25 Bell 15 binomial 10 15 21 + 998977951 c.decagonal 361 451 551 + 998637781 c.heptagonal 253 841 26797 + 999694151 c.nonagonal 10 253 703 + 998977951 c.octagonal 25 49 121 + 999002449 c.pentagonal 391 1501 1891 + 996852481 c.square 25 221 481 + 999894481 c.triangular 10 361 901 + 993551149 cake 15 299 697 Catalan 14 congruent 14 15 21 + 9999727 constructible 10 15 Cullen 25 Cunningham 10 15 35 + 998307217 Curzon 14 21 209 + 199998101 cyclic 15 35 143 + 9999811 D-number 15 21 d-powerful 209 377 407 + 9988337 de Polignac 1207 1271 1541 + 99400891 decagonal 10 451 1387 + 990061957 deceptive 451 481 703 + 999670027 deficient 10 14 15 + 9999811 dig.balanced 10 15 21 + 199983713 double fact. 15 Duffinian 21 25 35 + 9999811 economical 10 14 15 + 19999979 emirpimes 15 49 143 + 99460729 equidigital 10 14 15 + 19999979 eRAP 26123 1572827 9625397 + 886859719 esthetic 10 21 121 + 989878789 Eulerian 247 evil 10 15 169 + 999999859 fibodiv 14 323 130901 609999623 Fibonacci 21 377 121393 5702887 Friedman 25 121 289 + 966289 frugal 1369 1681 1849 + 999002449 gapful 121 143 187 + 2059 Gilda 49 happy 10 49 319 + 9999697 Harshad 10 21 209 + 1679 heptagonal 403 697 2059 + 999670027 hex 169 817 1027 + 998038081 hexagonal 15 703 1891 + 980957071 hoax 319 361 391 + 97333987 Hogben 21 703 871 + 999413383 hyperperfect 21 697 1333 + 974380921 iban 10 14 21 + 774443 idoneal 10 15 21 + 253 inconsummate 377 493 527 + 968087 interprime 15 21 473 + 98244719 Jacobsthal 21 341 22369621 junction 319 517 713 + 98962343 Kaprekar 703 5072059 katadrome 10 21 731 + 9876431 Kynea 4198399 268468223 Lehmer 15 247 451 + 998849281 Leyland 1649 lonely 1343 Lucas 64079 4870847 lucky 15 21 25 + 9999811 Lynch-Bell 15 magic 15 671 magnanimous 14 21 25 + 22600601 metadrome 14 15 25 + 234679 modest 49 209 299 + 999511111 Moran 21 209 247 + 1679 Motzkin 21 323 narcissistic 407 nialpdrome 10 21 221 + 999999863 nonagonal 559 41311 85879 + 979466221 nude 15 oban 10 15 25 + 989 octagonal 21 341 481 + 999260501 odious 14 21 25 + 999999863 palindromic 121 323 737 + 999949999 pancake 121 407 529 + 998173541 panconsummate 10 14 15 + 481 pandigital 15 21 partition 15 2679689 pentagonal 35 247 1247 + 993885751 pernicious 10 14 21 + 9999811 Perrin 10 209 2627 plaindrome 14 15 25 + 888888899 Poulet 341 1387 2047 + 998590601 power 25 49 121 + 999002449 powerful 25 49 121 + 999002449 primeval 1037 1079 103679 10023457 Proth 25 49 209 + 999653377 repfigit 14 1537 repunit 15 21 121 + 999413383 Rhonda 54479 256973 285359 + 858441359 Ruth-Aaron 15 25 49 + 967267387 self 121 143 187 + 999999467 self-describing 12193331 12311833 14313319 + 31151933 semiprime 10 14 15 + 99460729 sliding 25 Smith 121 319 391 + 97333987 square 25 49 121 + 999002449 star 121 253 793 + 998847037 straight-line 1357 56789 strobogrammatic 689 1691 1961 + 666808999 super Niven 10 super-d 169 247 319 + 9999557 tetrahedral 10 35 tetranacci 15 triangular 10 15 21 + 998977951 tribonacci 10609 trimorphic 25 49 uban 10 15 21 + 89000071 Ulam 209 221 253 + 10000153 undulating 121 323 737 + 38383 unprimeable 1293671 4134953 4749187 + 9298061 upside-down 1649 1739 1829 + 97691431 vampire 117067 124483 146137 + 79168819 wasteful 143 187 209 + 9999811 Wieferich 3837523 Woodall 323 2047 93749 90699263 Zuckerman 15 zygodrome 22999 55577 1166111 + 999997777