Sum of primes in odd positions is prime: Difference between revisions
→{{header|REXX}}: added the computer programming language REXX. |
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653 17959
823 26879</pre>
=={{header|REXX}}==
<lang REXX>/*REXX pgm shows a prime index, the prime, & sum of odd indexed primes when sum is prime*/
parse arg hi . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 1000 /*Not specified? Then use the default.*/
call genP /*build array of semaphores for primes.*/
title= 'odd indexed primes the sum of the odd indexed primes'
say ' index │'center(title, 65)
say '───────┼'center("" , 65, '─')
found= 0 /*initialize # of odd indexed primes···*/
$= 0 /*sum of odd indexed primes (so far). */
do j=1 by 2; p= @.j; if p>hi then leave /*find odd indexed primes, sum = prime.*/
$= $ + p /*add this odd index prime to the sum. */
if \!.$ then iterate /*This sum not prime? Then skip it. */
found= found + 1 /*bump the number of solutions found. */
say center(j, 7)'│' right( commas(p), 13) right( commas($), 33)
end /*j*/
say '───────┴'center("" , 65, '─')
say
say 'Found ' commas(found) ' 'subword(title, 1, 3)
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 /*define some low primes. */
!.=0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " semaphores. */
#=5; sq.#= @.# ** 2 /*number of primes so far; prime². */
do j=@.#+2 by 2 to hi*33; parse var j '' -1 _ /*obtain the last decimal dig.*/
if _==5 then iterate; if j//3==0 then iterate; if j//7==0 then iterate
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# */
end /*j*/; return</lang>
{{out|output|text= when using the default inputs:}}
<pre>
index │ odd indexed primes the sum of the odd indexed primes
───────┼─────────────────────────────────────────────────────────────────
1 │ 2 2
3 │ 5 7
11 │ 31 89
27 │ 103 659
35 │ 149 1,181
67 │ 331 5,021
91 │ 467 9,923
95 │ 499 10,909
99 │ 523 11,941
119 │ 653 17,959
143 │ 823 26,879
───────┴─────────────────────────────────────────────────────────────────
Found 11 odd indexed primes
</pre>
=={{header|Ring}}==
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Revision as of 20:45, 1 September 2021
- Task
Let p(i) be a sequence of prime numbers.
Consider the p(1),p(3),p(5), ... ,p(i), for each p(i) < 1,000 and i is odd.
Let sum be the sum of these primes.
If sum is prime then print i, p(i) and sum.
Factor
<lang factor>USING: assocs assocs.extras kernel math.primes math.statistics prettyprint sequences.extras ;
1000 primes-upto <evens> dup cum-sum zip [ prime? ] filter-values .</lang>
- Output:
{ { 2 2 } { 5 7 } { 31 89 } { 103 659 } { 149 1181 } { 331 5021 } { 467 9923 } { 499 10909 } { 523 11941 } { 653 17959 } { 823 26879 } }
Go
<lang go>package main
import (
"fmt" "rcu"
)
func main() {
primes := rcu.Primes(999) sum := 0 fmt.Println(" i p[i] Σp[i]") fmt.Println("----------------") for i := 0; i < len(primes); i += 2 { sum += primes[i] if rcu.IsPrime(sum) { fmt.Printf("%3d %3d %6s\n", i+1, primes[i], rcu.Commatize(sum)) } }
}</lang>
- Output:
i p[i] Σp[i] ---------------- 1 2 2 3 5 7 11 31 89 27 103 659 35 149 1,181 67 331 5,021 91 467 9,923 95 499 10,909 99 523 11,941 119 653 17,959 143 823 26,879
Nim
<lang Nim>import strformat
template isOdd(n: Natural): bool = (n and 1) != 0 template isEven(n: Natural): bool = (n and 1) == 0
func isPrime(n: Positive): bool =
if n == 1: return false if n.isEven: return n == 2 if n mod 3 == 0: return n == 3 var d = 5 while d * d <= n: if n mod d == 0: return false inc d, 2 if n mod d == 0: return false inc d, 4 result = true
- Compute the sums of primes at odd position.
echo " i p(i) sum" var idx = 0 var sum = 0 var p = 1 while p < 1000:
inc p if p.isPrime: inc idx if idx.isOdd: inc sum, p if sum.isPrime: echo &"{idx:3} {p:3} {sum:5}"</lang>
- Output:
i p(i) sum 1 2 2 3 5 7 11 31 89 27 103 659 35 149 1181 67 331 5021 91 467 9923 95 499 10909 99 523 11941 119 653 17959 143 823 26879
Phix
with javascript_semantics sequence primes = get_primes_le(1000) integer total = 0 printf(1," i p sum\n") printf(1,"----------------\n") for i=1 to length(primes) by 2 do total += primes[i] if is_prime(total) then printf(1,"%3d %3d %,6d\n", {i, primes[i], total}) end if end for
- Output:
i p sum ---------------- 1 2 2 3 5 7 11 31 89 27 103 659 35 149 1,181 67 331 5,021 91 467 9,923 95 499 10,909 99 523 11,941 119 653 17,959 143 823 26,879
Raku
<lang perl6>my @odd = grep { ++$ !%% 2 }, grep &is-prime, 2 ..^ 1000; my @sums = [\+] @odd;
say .fmt('%5d') for grep { .[1].is-prime }, ( @odd Z @sums );</lang>
- Output:
2 2 5 7 31 89 103 659 149 1181 331 5021 467 9923 499 10909 523 11941 653 17959 823 26879
REXX
<lang REXX>/*REXX pgm shows a prime index, the prime, & sum of odd indexed primes when sum is prime*/ parse arg hi . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 1000 /*Not specified? Then use the default.*/ call genP /*build array of semaphores for primes.*/
title= 'odd indexed primes the sum of the odd indexed primes'
say ' index │'center(title, 65) say '───────┼'center("" , 65, '─') found= 0 /*initialize # of odd indexed primes···*/ $= 0 /*sum of odd indexed primes (so far). */
do j=1 by 2; p= @.j; if p>hi then leave /*find odd indexed primes, sum = prime.*/ $= $ + p /*add this odd index prime to the sum. */ if \!.$ then iterate /*This sum not prime? Then skip it. */ found= found + 1 /*bump the number of solutions found. */ say center(j, 7)'│' right( commas(p), 13) right( commas($), 33) end /*j*/
say '───────┴'center("" , 65, '─') say say 'Found ' commas(found) ' 'subword(title, 1, 3) 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 /*define some low primes. */
!.=0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " semaphores. */ #=5; sq.#= @.# ** 2 /*number of primes so far; prime². */ do j=@.#+2 by 2 to hi*33; parse var j -1 _ /*obtain the last decimal dig.*/ if _==5 then iterate; if j//3==0 then iterate; if j//7==0 then iterate 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# */ end /*j*/; return</lang>
- output when using the default inputs:
index │ odd indexed primes the sum of the odd indexed primes ───────┼───────────────────────────────────────────────────────────────── 1 │ 2 2 3 │ 5 7 11 │ 31 89 27 │ 103 659 35 │ 149 1,181 67 │ 331 5,021 91 │ 467 9,923 95 │ 499 10,909 99 │ 523 11,941 119 │ 653 17,959 143 │ 823 26,879 ───────┴───────────────────────────────────────────────────────────────── Found 11 odd indexed primes
Ring
<lang ring> load "stdlib.ring" see "working..." + nl see "i p sum" + nl
nr = 0 sum = 0 limit = 1000
for n = 2 to limit
if isprime(n) nr++ if nr%2 = 1 sum += n if isprime(sum) see "" + nr + " " + n + " " + sum + nl ok ok ok
next
see "done..." + nl </lang>
- Output:
working... i p sum 1 2 2 3 5 7 11 31 89 27 103 659 35 149 1181 67 331 5021 91 467 9923 95 499 10909 99 523 11941 119 653 17959 143 823 26879 done...
Wren
<lang ecmascript>import "/math" for Int import "/trait" for Indexed import "/fmt" for Fmt
var primes = Int.primeSieve(999) var sum = 0 System.print(" i p[i] Σp[i]") System.print("----------------") for (se in Indexed.new(primes, 2)) {
sum = sum + se.value if (Int.isPrime(sum)) Fmt.print("$3d $3d $,6d", se.index + 1, se.value, sum)
}</lang>
- Output:
i p[i] Σp[i] ---------------- 1 2 2 3 5 7 11 31 89 27 103 659 35 149 1,181 67 331 5,021 91 467 9,923 95 499 10,909 99 523 11,941 119 653 17,959 143 823 26,879
XPL0
<lang XPL0>func IsPrime(N); \Return 'true' if N is a prime number int N, I; [if N <= 1 then return false; for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true; ];
int I, Sum, N; [Text(0, "p(n) sum^m^j"); Sum:= 0; I:= 0; for N:= 2 to 1000-1 do
[if IsPrime(N) then [I:= I+1; if I&1 then \odd [Sum:= Sum + N; if IsPrime(Sum) then [IntOut(0, N); ChOut(0, ^ ); IntOut(0, Sum); CrLf(0)]; ]; ]; ];
]</lang>
- Output:
p(n) sum 2 2 5 7 31 89 103 659 149 1181 331 5021 467 9923 499 10909 523 11941 653 17959 823 26879