Sum of primes in odd positions is prime
- 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 summarize of these primes.
If sum is prime then print 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
Ring
<lang ring> load "stdlib.ring" see "working..." + nl see "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 "" + n + " " + sum + nl
ok
ok
ok
next
see "done..." + nl </lang>
- Output:
working... p sum 2 2 5 7 31 89 103 659 149 1181 331 5021 467 9923 499 10909 523 11941 653 17959 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