Prime numbers p for which the sum of primes less than or equal to p is prime: Difference between revisions
Content added Content deleted
(Added Go) |
(→{{header|REXX}}: added the computer programming language REXX.) |
||
Line 58: | Line 58: | ||
<pre> |
<pre> |
||
21 found: {2,3,7,13,37,43,281,311,503,541,557,593,619,673,683,733,743,839,881,929,953} |
21 found: {2,3,7,13,37,43,281,311,503,541,557,593,619,673,683,733,743,839,881,929,953} |
||
</pre> |
|||
=={{header|REXX}}== |
|||
<lang rexx>/*REXX program finds primes in which sum of primes ≤ P is prime, where P < 1.000.*/ |
|||
parse arg hi cols . /*obtain optional argument from the CL.*/ |
|||
if hi=='' | hi=="," then hi= 1000 /*Not specified? Then use the default.*/ |
|||
if cols=='' | cols=="," then cols= 10 /* " " " " " " */ |
|||
call genP /*build array of semaphores for primes.*/ |
|||
w= 10 /*the width of a number in any column. */ |
|||
title= ' primes which the sum of primes ≤ P is prime, where P < ' commas(hi) |
|||
say ' index │' center(title, 1 + cols*(w+1) ) |
|||
say '───────┼'center("" , 1 + cols*(w+1), '─') |
|||
found= 0; idx = 1 /*number of primes found (so far); IDX.*/ |
|||
$=; pSum= 0 /*#: list of primes (so far); init pSum*/ |
|||
do j=1 for hi-1; p= @.j; pSum= pSum+p /*find summation primes within range. */ |
|||
if \!.pSum then iterate /*Is sum─of─primes a prime? Then skip.*/ |
|||
found= found + 1 /*bump the number of found primes. */ |
|||
if cols<0 then iterate /*Build the list (to be shown later)? */ |
|||
c= commas(p) /*maybe add commas to the number. */ |
|||
$= $ right(c, max(w, length(c) ) ) /*add a found prime──►list, allow big #*/ |
|||
if found//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 /*j*/ |
|||
say '───────┴'center("" , 1 + cols*(w+1), '─') |
|||
say |
|||
say 'Found ' commas(found) title |
|||
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: !.= 0; sP= 0 /*prime semaphores; sP= sum of primes.*/ |
|||
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */ |
|||
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */ |
|||
#=5; sq.#= @.# **2 /*number of primes so far; prime². */ |
|||
/* [↓] generate more primes ≤ high.*/ |
|||
do j=@.#+2 by 2 until @.#>=hi & @.#>sP /*find odd primes where P≥hi and P>sP.*/ |
|||
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? */ |
|||
do k=5 while sq.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; sq.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */ |
|||
if @.#<hi then sP= sP + @.# /*maybe add this prime to sum─of─primes*/ |
|||
end /*j*/; return</lang rexx> |
|||
{{out|output|text= when using the default inputs:}} |
|||
<pre> |
|||
index │ primes which the sum of primes ≤ P is prime, where P < 1,000 |
|||
───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
|||
1 │ 2 3 7 13 37 43 281 311 503 541 |
|||
11 │ 557 593 619 673 683 733 743 839 881 929 |
|||
───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── |
|||
Found 21 primes which the sum of primes ≤ P is prime, where P < 1,000 |
|||
</pre> |
</pre> |
||