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Special odd numbers: Difference between revisions
→{{header|REXX}}: added the computer programming language REXX.
(→{{header|REXX}}: added the computer programming language REXX.) |
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933 939 943 949 951 955 959 965 973 979 985 989 993 995
</pre>
=={{header|REXX}}==
<lang rexx>/*REXX program finds 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= ' 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 squarefree semiprimes. */
do j=2 while @.j < hi /*generate 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 /*the number of 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 squarefree 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 a Frobenius #──►list, 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>
{{out|output|text= when using the default inputs:}}
<pre>
index │ 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 squarefree semiprimes < 1,000
</pre>
=={{header|Ring}}==
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