Brilliant numbers
Brilliant numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Brilliant numbers are a subset of semiprime numbers. Specifically, they are numbers that are the product of exactly two prime numbers that both have the same number of digits when expressed in base 10.
Brilliant numbers are useful in cryptography and when testing prime factoring algorithms.
- E.G.
- 3 × 3 (9) is a brilliant number.
- 2 × 7 (14) is a brilliant number.
- 113 × 691 (78083) is a brilliant number.
- 2 × 31 (62) is semiprime, but is not a brilliant number (different number of digits in the two factors).
- Task
- Find and display the first 100 brilliant numbers.
- For the orders of magnitude 2 through 6, find and show the first brilliant number greater than or equal to than the order of magnitude, and, its position in the series (or the count of brilliant numbers up to that point).
- Stretch
- Continue for larger orders of magnitude.
- See also
Raku
2 through 7 are fast. 8 and 9 take a bit longer. <lang perl6>use Lingua::EN::Numbers;
- Find an abundance of primes to use to generate brilliants
my %primes = (2..100000).grep( &is-prime ).categorize: { .chars };
- Generate brilliant numbers
my @brilliant = lazy flat (1..*).map: -> $digits {
sort flat (^%primes{$digits}).race.map: { %primes{$digits}[$_] X× (flat %primes{$digits}[$_ .. *]) }
};
- Testing
put "First 100 brilliant numbers:\n" ~ @brilliant[^100].batch(10)».fmt("%4d").join("\n") ~ "\n" ;
for 1 .. 7 -> $e {
my $threshold = exp $e, 10;
my $key = @brilliant.first: :k, * >= exp $e, 10;
say "First term >= than {comma $threshold} is {ordinal-digit 1 + $key} in the series: {comma @brilliant[$key]}";
}</lang>
- Output:
First 100 brilliant numbers: 4 6 9 10 14 15 21 25 35 49 121 143 169 187 209 221 247 253 289 299 319 323 341 361 377 391 403 407 437 451 473 481 493 517 527 529 533 551 559 583 589 611 629 649 667 671 689 697 703 713 731 737 767 779 781 793 799 803 817 841 851 869 871 893 899 901 913 923 943 949 961 979 989 1003 1007 1027 1037 1067 1073 1079 1081 1121 1139 1147 1157 1159 1189 1207 1219 1241 1247 1261 1271 1273 1333 1343 1349 1357 1363 1369 First term >= than 10 is 4th in the series: 10 First term >= than 100 is 11th in the series: 121 First term >= than 1,000 is 74th in the series: 1,003 First term >= than 10,000 is 242nd in the series: 10,201 First term >= than 100,000 is 2505th in the series: 100,013 First term >= than 1,000,000 is 10538th in the series: 1,018,081 First term >= than 10,000,000 is 124364th in the series: 10,000,043 First term >= than 100,000,000 is 573929th in the series: 100,140,049 First term >= than 1,000,000,000 is 7407841st in the series: 1,000,000,081