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How to find two prime numbers that, when concatenated, form another prime number in Swift

1 Answer

0 votes
import Foundation

func isPrime(_ n: Int64) -> Bool {
    if n < 2 { return false }
    if n % 2 == 0 && n != 2 { return false }

    var i: Int64 = 3
    while i * i <= n {
        if n % i == 0 { return false }
        i += 2
    }
    return true
}

// Concatenate two integers
func concat(_ a: Int, _ b: Int) -> Int64 {
    let s = "\(a)\(b)"
    return Int64(s)!
}

func main() {
    let limit = 12 // you can increase this
    var primes: [Int] = []

    // Generate primes up to limit
    for i in 2...limit {
        if isPrime(Int64(i)) {
            primes.append(i)
        }
    }

    // Check pairs
    for i in primes.indices {
        for j in primes.indices {
            if i == j { continue } // skip same prime if you want
            let num = concat(primes[i], primes[j])
            if isPrime(num) {
                print("\(primes[i]) + \(primes[j]) -> \(num) is prime")
            }
        }
    }
}

main()



/*
run:

2 + 3 -> 23 is prime
2 + 11 -> 211 is prime
3 + 7 -> 37 is prime
3 + 11 -> 311 is prime
5 + 3 -> 53 is prime
7 + 3 -> 73 is prime
11 + 3 -> 113 is prime

*/

 



answered Nov 28, 2025 by avibootz
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