Special odd numbers
Odd numbers of the form p*q where p and q are distinct primes, where p*q < 1000
- Task
Factor
<lang factor>USING: combinators.short-circuit formatting grouping io kernel math.primes.factors math.ranges prettyprint sequences sets ;
- sq-free-semiprime? ( n -- ? )
factors { [ length 2 = ] [ all-unique? ] } 1&& ;
- odd-sfs-upto ( n -- seq )
1 swap 2 <range> [ sq-free-semiprime? ] filter ;
999 odd-sfs-upto dup length "Found %d odd square-free semiprimes < 1000:\n" printf 20 group [ [ "%4d" printf ] each nl ] each nl</lang>
- Output:
Found 194 odd square-free semiprimes < 1000: 15 21 33 35 39 51 55 57 65 69 77 85 87 91 93 95 111 115 119 123 129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219 221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323 327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427 437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527 533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633 635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723 731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815 817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923 933 939 943 949 951 955 959 965 973 979 985 989 993 995
Julia
<lang julia>using Primes
twoprimeproduct(n) = (a = factor(n).pe; length(a) == 2 && all(p -> p[2] == 1, a))
special1k = filter(n -> isodd(n) && twoprimeproduct(n), 1:1000)
foreach(p -> print(rpad(p[2], 4), p[1] % 20 == 0 ? "\n" : ""), enumerate(special1k))
</lang>
- Output:
15 21 33 35 39 51 55 57 65 69 77 85 87 91 93 95 111 115 119 123 129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219 221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323 327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427 437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527 533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633 635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723 731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815 817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923 933 939 943 949 951 955 959 965 973 979 985 989 993 995
REXX
<lang rexx>/*REXX pgm finds odd squarefree semiprimes (product of 2 primes) that are less then N. */ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 1000 /* " " " " " " */ if cols== | cols=="," then cols= 10 /* " " " " " " */ call genP /*build array of semaphores for primes.*/ w= 10 /*width of a number in any column. */
@sss= ' odd squarefree semiprimes < ' commas(1000)
if cols>0 then say ' index │'center(@sss, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') idx= 1 /*initialize the index of output lines.*/ $=; ss.= 0 /*a list of odd squarefree semiprimes. */
do j=2 while @.j < hi /*gen odd squarefree semiprimes < HI.*/
do k=j+1 while @.k < hi /*ensure primes are squarefree & < HI.*/
_= @.j * @.k /*calculate the product of 2 odd primes*/
if _>=hi then leave /*Is the product ≥ HI? Then skip it. */
ss._= 1 /*mark # as being squarefree semiprime.*/
end /*k*/
end /*j*/
sss= 0 /*number of odd squarefree semiprimes. */
do m=3 by 2 to hi-1 /*search a list of possible candicates.*/
if \ss.m then iterate /*Does this number exist? No, skip it.*/
sss= sss + 1 /*bump count of odd sq─free semiprimes.*/
if cols==0 then iterate /*Build the list (to be shown later)? */
c= commas(m) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add odd sq─free semiprime, allow big#*/
if sss//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*m*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ say say 'Found ' commas(sss) @sss exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6= 13 /*define some low primes. */
#=6; s.#= @.# **2 /*number of primes so far; prime²*/
/* [↓] generate more primes ≤ high.*/
do j=@.#+4 by 2 to hi+1 /*find odd primes from here on. */
parse var j -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
if j//11==0 then iterate /*" " " 11? */
/* [↑] the above four lines saves time*/
do k=6 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j /*bump # Ps; assign next P; P squared*/
end /*j*/; return</lang>
- output when using the default inputs:
index │ odd squarefree semiprimes < 1,000 ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 15 21 33 35 39 51 55 57 65 69 11 │ 77 85 87 91 93 95 111 115 119 123 21 │ 129 133 141 143 145 155 159 161 177 183 31 │ 185 187 201 203 205 209 213 215 217 219 41 │ 221 235 237 247 249 253 259 265 267 287 51 │ 291 295 299 301 303 305 309 319 321 323 61 │ 327 329 335 339 341 355 365 371 377 381 71 │ 391 393 395 403 407 411 413 415 417 427 81 │ 437 445 447 451 453 469 471 473 481 485 91 │ 489 493 497 501 505 511 515 517 519 527 101 │ 533 535 537 543 545 551 553 559 565 573 111 │ 579 581 583 589 591 597 611 623 629 633 121 │ 635 649 655 667 669 671 679 681 685 687 131 │ 689 695 697 699 703 707 713 717 721 723 141 │ 731 737 745 749 753 755 763 767 771 779 151 │ 781 785 789 791 793 799 803 807 813 815 161 │ 817 831 835 843 849 851 865 869 871 879 171 │ 889 893 895 899 901 905 913 917 921 923 181 │ 933 939 943 949 951 955 959 965 973 979 191 │ 985 989 993 995 Found 194 odd squarefree semiprimes < 1,000
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl see "Special odd numbers are:" + nl
row = 0 limit1 = 150 Prim = []
for n = 1 to limit1
for m = n+1 to limit1-1
if isprime(n) and isprime(m)
prod = n*m
if prod%2 = 1
add(Prim,prod)
ok
ok
next
next
Prim = sort(Prim) for n = 1 to len(Prim)
if Prim[n] > 1000
n = n - 1
exit
ok
see "" + Prim[n] + " "
if n%10 = 0
see nl
ok
next
see nl + "Found " + n + " Special odd numbers." + nl see "done..." + nl </lang>
- Output:
working... Special odd numbers are: 15 21 33 35 39 51 55 57 65 69 77 85 87 91 93 95 111 115 119 123 129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219 221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323 327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427 437 445 447 451 469 473 481 485 493 497 505 511 515 517 527 533 535 545 551 553 559 565 581 583 589 611 623 629 635 649 655 667 671 679 685 689 695 697 703 707 713 721 731 737 745 749 763 767 779 781 791 793 799 803 817 851 869 871 889 893 899 901 913 917 923 943 949 959 973 979 989 Found 151 Special odd numbers. done...