Summation of primes
- Task
The task description is taken from Project Euler (https://projecteuler.net/problem=10)
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17
Find the sum of all the primes below two million
ALGOL 68
<lang algol68>BEGIN # sum primes up to 2 000 000 #
PR read "primes.incl.a68" PR
# return s space-separated into groups of 3 digits #
PROC space separate = ( STRING unformatted )STRING:
BEGIN
STRING result := "";
INT ch count := 0;
FOR c FROM UPB unformatted BY -1 TO LWB unformatted DO
IF ch count <= 2 THEN ch count +:= 1
ELSE ch count := 1; " " +=: result
FI;
unformatted[ c ] +=: result
OD;
result
END # space separate # ;
# sum the primes #
[]BOOL prime = PRIMESIEVE 2 000 000;
LONG INT sum := 2;
FOR i FROM 3 BY 2 TO UPB prime DO
IF prime[ i ] THEN
sum +:= i
FI
OD;
print( ( space separate( whole( sum, 0 ) ), newline ) )
END</lang>
- Output:
142 913 828 922
AWK
<lang AWK>
- syntax: GAWK -f SUMMATION_OF_PRIMES.AWK
BEGIN {
main(10) main(2000000) exit(0)
} function main(stop, count,sum) {
if (stop < 3) {
return
}
count = 1
sum = 2
for (i=3; i<stop; i+=2) {
if (is_prime(i)) {
sum += i
count++
}
}
printf("The %d primes below %d sum to %d\n",count,stop,sum)
} function is_prime(n, d) {
d = 5
if (n < 2) { return(0) }
if (n % 2 == 0) { return(n == 2) }
if (n % 3 == 0) { return(n == 3) }
while (d*d <= n) {
if (n % d == 0) { return(0) }
d += 2
if (n % d == 0) { return(0) }
d += 4
}
return(1)
} </lang>
- Output:
The 4 primes below 10 sum to 17 The 148933 primes below 2000000 sum to 142913828922
BASIC
FreeBASIC
<lang freebasic>#include "isprime.bas"
dim as integer sum = 2, i, n=1 for i = 3 to 2000000 step 2
if isprime(i) then
sum += i
n+=1
end if
next i
print sum</lang>
- Output:
142913828922
GW-BASIC
<lang gwbasic>10 S# = 2 20 FOR P = 3 TO 1999999! STEP 2 30 GOSUB 80 40 IF Q=1 THEN S#=S#+P 50 NEXT P 60 PRINT S# 70 END 80 Q=0 90 IF P=3 THEN Q=1:RETURN 100 I=1 110 I=I+2 120 IF INT(P/I)*I = P THEN RETURN 130 IF I*I<=P THEN GOTO 110 140 Q = 1 150 RETURN </lang>
- Output:
142913828922
C
<lang c>#include<stdio.h>
- include<stdlib.h>
int isprime( int p ) {
int i;
if(p==2) return 1;
if(!(p%2)) return 0;
for(i=3; i*i<=p; i+=2) {
if(!(p%i)) return 0;
}
return 1;
}
int main( void ) {
int p;
long int s = 2;
for(p=3;p<2000000;p+=2) {
if(isprime(p)) s+=p;
}
printf( "%ld\n", s );
return 0;
}</lang>
- Output:
142913828922
CLU
<lang clu>isqrt = proc (s: int) returns (int)
x0: int := s/2
if x0=0 then
return(s)
else
x1: int := (x0 + s/x0) / 2
while x1<x0 do
x0 := x1
x1 := (x0 + s/x0) / 2
end
return(x0)
end
end isqrt
sieve = proc (top: int) returns (array[bool])
prime: array[bool] := array[bool]$fill(2,top-1,true)
for p: int in int$from_to(2,isqrt(top)) do
for c: int in int$from_to_by(p*p,top,p) do
prime[c] := false
end
end
return(prime)
end sieve
sum_primes_to = proc (top: int) returns (int)
sum: int := 0
prime: array[bool] := sieve(top)
for i: int in array[bool]$indexes(prime) do
if prime[i] then sum := sum+i end
end
return(sum)
end sum_primes_to
start_up = proc ()
stream$putl(stream$primary_output(), int$unparse(sum_primes_to(2000000)))
end start_up </lang>
- Output:
142913828922
Crystal
<lang ruby>def prime?(n) # P3 Prime Generator primality test
return false unless (n | 1 == 3 if n < 5) || (n % 6) | 4 == 5 sqrt_n = Math.isqrt(n) pc = typeof(n).new(5) while pc <= sqrt_n return false if n % pc == 0 || n % (pc + 2) == 0 pc += 6 end true
end
puts "The sum of all primes below 2 million is #{(0i64..2000000i64).select { |n| n if prime? n }.sum}."
</lang>
- Output:
The sum of all primes below 2 million is 142913828923.
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // Summation of primes. Nigel Galloway: November 9th., 2021 printfn $"%d{primes64()|>Seq.takeWhile((>)2000000L)|>Seq.sum}" </lang>
- Output:
142913828922
Factor
<lang factor>USING: math.primes prettyprint sequences ;
2,000,000 primes-upto sum .</lang>
- Output:
142913828922
Fermat
<lang fermat>s:=2; for p=3 to 1999999 by 2 do if Isprime(p) then s:=s+p fi od; !!s;</lang>
- Output:
142913828922
Go
<lang go>package main
import (
"fmt" "rcu"
)
func main() {
sum := 0
for _, p := range rcu.Primes(2e6 - 1) {
sum += p
}
fmt.Printf("The sum of all primes below 2 million is %s.\n", rcu.Commatize(sum))
}</lang>
- Output:
The sum of all primes below 2 million is 142,913,828,922.
jq
Works with gojq, the Go implementation of jq
See Erdős-primes#jq for a suitable definition of `is_prime/1` as used here. <lang jq>def sum(s): reduce s as $x (0; .+$x);
sum(2, range(3 ; 2E6; 2) | select(is_prime))</lang>
- Output:
142913828922
Julia
<lang julia>using Primes
@show sum(primes(2_000_000)) # sum(primes(2000000)) = 142913828922 </lang>
Mathematica / Wolfram Language
<lang Mathematica>Total[Most@NestWhileList[NextPrime, 2, # < 2000000 &]]</lang>
- Output:
142913828922
PARI/GP
<lang parigp> s=2; p=3 while(p<2000000,if(isprime(p),s=s+p);p=p+2) print(s) </lang>
- Output:
142913828922
Pascal
uses
<lang pascal> program SumPrimes; {$IFDEF FPC}{$MODE DELPHI}{$OPTIMIZATION ON,ALL} {$ELSE} {$APPTYPE CONSOLE} {$ENDIF} uses
SysUtils,primTrial;
var
p,sum : NativeInt;
begin
sum := actPrime;
repeat inc(sum,p); p := NextPrime until p >= 2*1000*1000;
writeln(sum);
{$IFDEF WINDOWS} readln;{$ENDIF}
end.</lang>
- Output:
142913828922
Perl
<lang perl>#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Summation_of_primes use warnings; use ntheory qw( primes ); use List::Util qw( sum );
print sum( @{ primes( 2e6 ) } ), "\n";</lang>
- Output:
142913828922
Phix
printf(1,"The sum of primes below 2 million is %,d\n",sum(get_primes_le(2e6)))
- Output:
The sum of primes below 2 million is 142,913,828,922
Python
<lang python>#!/usr/bin/python
def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
if __name__ == '__main__':
suma = 2
n = 1
for i in range(3, 2000000, 2):
if isPrime(i):
suma += i
n+=1
print(suma)</lang>
- Output:
142913828922
Raku
Slow, but only using compiler built-ins (about 5 seconds) <lang perl6>say sum (^2e6).grep: {.&is-prime};</lang>
- Output:
142913828922
Much faster using external libraries (well under half a second) <lang perl6>use Math::Primesieve; my $sieve = Math::Primesieve.new; say sum $sieve.primes(2e6.Int);</lang> Same output
Ring
<lang ring> load "stdlib.ring" see "working..." + nl sum = 2 limit = 2000000
for n = 3 to limit step 2
if isprime(n)
sum += n
ok
next
see "The sum of all the primes below two million:" + nl see "" + sum + nl see "done..." + nl </lang>
- Output:
working... The sum of all the primes below two million: 142,913,828,922 done...
Ruby
<lang ruby>puts Prime.each(2_000_000).sum </lang>
- Output:
142913828922
Wren
<lang ecmascript>import "./math" for Int, Nums import "./fmt" for Fmt
Fmt.print("The sum of all primes below 2 million is $,d.", Nums.sum(Int.primeSieve(2e6-1)))</lang>
- Output:
The sum of all primes below 2 million is 142,913,828,922.
XPL0
Takes 3.7 seconds on Pi4. <lang XPL0>func IsPrime(N); \Return 'true' if N is a prime number >= 3 int N, I; [if (N&1) = 0 then return false; \N is even for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false; I:= I+1; \step by 2 (=1+1) ];
return true; ];
real Sum; \provides 15 decimal digits int N; \provides 9 decimal digits [Sum:= 2.; \2 is prime for N:= 3 to 2_000_000 do
if IsPrime(N) then Sum:= Sum + float(N);
Format(1, 0); \don't show places after decimal point RlOut(0, Sum); ]</lang>
- Output:
142913828922