Data update
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Ingy dot Net
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1045 changed files with 18889 additions and 2777 deletions
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/*REXX program counts/displays the number of additive primes under a specified number N.*/
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parse arg n cols . /*get optional number of primes to find*/
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if n=='' | n=="," then n= 500 /*Not specified? Then assume default.*/
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if cols=='' | cols=="," then cols= 10 /* " " " " " */
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call genP n /*generate all primes under N. */
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w= 10 /*width of a number in any column. */
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title= " additive primes that are < " commas(n)
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if cols>0 then say ' index │'center(title, 1 + cols*(w+1) )
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if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
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found= 0; idx= 1 /*initialize # of additive primes & IDX*/
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$= /*a list of additive primes (so far). */
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do j=1 for #; p= @.j /*obtain the Jth prime. */
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_= sumDigs(p); if \!._ then iterate /*is sum of J's digs a prime? No, skip.*/ /* ◄■■■■■■■■ a filter. */
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found= found + 1 /*bump the count of additive primes. */
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if cols<0 then iterate /*Build the list (to be shown later)? */
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c= commas(p) /*maybe add commas to the number. */
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$= $ right(c, max(w, length(c) ) ) /*add additive prime──►list, allow big#*/
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if found//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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/*REXX program counts/displays the number of additive primes less than N. */
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Parse Arg n cols . /*get optional number of primes To find*/
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If n=='' | n==',' Then n= 500 /*Not specified? Then assume default.*/
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If cols=='' | cols==',' Then cols= 10 /* ' ' ' ' ' */
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call genP n /*generate all primes under N. */
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w=5 /*width of a number in any column. */
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title= 'additive primes that are < 'commas(n)
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If cols>0 Then Say ' index ¦'center(title,cols*(w+1)+1)
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If cols>0 Then Say '-------+'center('' ,cols*(w+1)+1,'-')
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found=0
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ol='' /*a list of additive primes (so far). */
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idx=1
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Do j=1 By 1
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p=p.j /*obtain the Jth prime. */
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If p>n Then Leave /* no more needed */
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_=sumDigs(p)
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If !._ Then Do
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found=found+1 /*bump the count of additive primes. */
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c=commas(p) /*maybe add commas To the number. */
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ol=ol right(c,max(w,length(c))) /*add additive prime--?list,allow big# */
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If words(ol)=10 Then Do /* a line is complete */
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Say center(idx,7)'¦' substr(ol,2) /*display what we have so far (cols). */
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ol='' /* prepare for next line */
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idx=idx+10
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End
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End
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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(found) title
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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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sumDigs: parse arg x 1 s 2; do k=2 for length(x)-1; s= s + substr(x,k,1); end; return s
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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genP: parse arg n; @.1= 2; @.2= 3; @.3= 5; @.4= 7; @.5= 11; @.6= 13
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!.= 0; !.2= 1; !.3= 1; !.5= 1; !.7= 1; !.11= 1; !.13= 1
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#= 6; sq.#= @.# ** 2 /*the number of primes; prime squared.*/
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do j=@.#+2 by 2 for max(0, n%2-@.#%2-1) /*find odd primes from here on. */
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parse var j '' -1 _ /*obtain the last digit of the J var.*/
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if _==5 then iterate; if j// 3==0 then iterate /*J ÷ by 5? J ÷ by 3? */
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if j// 7==0 then iterate; if j//11==0 then iterate /*" " " 7? " " " 11? */
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/* [↓] divide by the primes. ___ */
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do k=6 while sq.k<=j /*divide J by other primes ≤ √ J */
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if j//@.k==0 then iterate j /*÷ by prev. prime? ¬prime ___ */
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end /*k*/ /* [↑] only divide up to √ J */
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#= # + 1; @.#= j; sq.#= j*j; !.j= 1 /*bump prime count; assign prime & flag*/
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end /*j*/; return
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If ol\=='' Then
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Say center(idx,7)'¦' substr(ol,2) /*possible display residual output. */
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If cols>0 Then
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Say '--------'center('',cols*(w+1)+1,'-')
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Say
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Say 'found ' commas(found) title
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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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sumDigs:Parse Arg x 1 s 2; Do k=2 For length(x)-1; s=s+substr(x,k,1); End; Return s
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/*--------------------------------------------------------------------------------*/
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genP:
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Parse Arg n
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pl=2 3 5 7 11 13
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!.=0
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Do np=1 By 1 While pl<>''
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Parse Var pl p pl
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p.np=p
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sq.np=p*p
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!.p=1
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End
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np=np-1
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Do j=p.np+2 by 2 While j<n
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Parse Var j '' -1 _ /*obtain the last digit of the J var.*/
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If _==5 Then Iterate
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If j// 3==0 Then Iterate
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If j// 7==0 Then Iterate
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If j//11==0 Then Iterate
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Do k=6 By 1 While sq.k<=j /*divide J by other primes <=sqrt(j) */
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If j//p.k==0 Then Iterate j /* not prime - try next */
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End /*k*/
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np=np+1 /*bump prime count; assign prime & flag*/
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p.np=j
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sq.np=j*j
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!.j=1
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End /*j*/
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Return
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