Neighbour primes: Difference between revisions
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(→{{header|REXX}}: added the computer programming language REXX.) |
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</pre> |
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=={{header|REXX}}== |
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<lang rexx>/*REXX program finds neighbor primes: P, Q, P*Q+2 are primes, and P < some specified N.*/ |
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parse arg hi cols . /*obtain optional argument from the CL.*/ |
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if hi=='' | hi=="," then hi= 500 /*Not specified? Then use the default.*/ |
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if cols=='' | cols=="," then cols= 10 /* " " " " " " */ |
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call genP hi+50 /*build semaphore array for low primes.*/ |
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do p=1 while @.p<hi |
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end /*p*/; lim= p-1; q= p+1 /*set LIM to prime for P; calc. 2nd HI.*/ |
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call genP @.p * @.q + 2 /*build semaphore array for high primes*/ |
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w= 10 /*width of a number in any column. */ |
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@neig= ' neighbor primes: p, q, p*q+2 are primes, and p < ' commas(hi) |
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if cols>0 then say ' index │'center(@neig, 1 + cols*(w+1) ) |
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if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') |
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Nprimes= 0; idx= 1 /*initialize # neighbor primes & index.*/ |
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$= /*a list of neighbor primes (so far).*/ |
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do j=1 to lim; jp= j+1; q= @.jp /*look for neighbor primes within range*/ |
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x= @.j * q + 2; if \!.x then iterate /*is X also a prime? No, then skip it.*/ |
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Nprimes= Nprimes + 1 /*bump the number of neighbor primes. */ |
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if cols==0 then iterate /*Build the list (to be shown later)? */ |
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$= $ right( commas(@.j), w) /*add neighbor prime ──► the $ list. */ |
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if Nprimes//cols\==0 then iterate /*have we populated a line of output? */ |
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say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */ |
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idx= idx + cols /*bump the index count for the output*/ |
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end /*j*/ |
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if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ |
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if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') |
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say |
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say 'Found ' commas(Nprimes) @neig |
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exit 0 /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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genP: !.= 0; parse arg limit /*placeholders for primes (semaphores).*/ |
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@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */ |
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!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */ |
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#=5; s.#= @.# **2 /*number of primes so far; prime². */ |
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/* [↓] generate more primes ≤ high.*/ |
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do j=@.#+2 by 2 to limit /*find odd primes from here on. */ |
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parse var j '' -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/ |
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if j// 3==0 then iterate /*" " " 3? */ |
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if j// 7==0 then iterate /*" " " 7? */ |
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/* [↑] the above 3 lines saves time.*/ |
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do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/ |
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if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */ |
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end /*k*/ /* [↑] only process numbers ≤ √ J */ |
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#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */ |
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end /*j*/; return</lang> |
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{{out|output|text= when using the default inputs:}} |
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<pre> |
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index │ neighbor primes: p, q, p*q+2 are primes, and p < 500 |
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───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
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1 │ 3 5 7 13 19 67 149 179 229 239 |
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11 │ 241 269 277 307 313 397 401 419 439 487 |
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───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
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Found 20 neighbor primes: p, q, p*q+2 are primes, and p < 500 |
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</pre> |
</pre> |
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