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Prime numbers p for which the sum of primes less than or equal to p is prime: Difference between revisions
Prime numbers p for which the sum of primes less than or equal to p is prime (view source)
Revision as of 19:56, 7 July 2021
, 2 years ago→{{header|REXX}}: added the computer programming language REXX.
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(→{{header|REXX}}: added the computer programming language REXX.) |
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<pre>
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>
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