Calculate Brun’s constant

Brun.swift

@main
public struct Brun {
    static let primesLength = 100000000

    public static func main() {
        
        // proven that all primes are in the form '6k +/- 1'
        // this is a switch to advance the candidate of +2 or +4, to be xored with 1 every loop.
        var form_6k_pm1 = false
        
        var primes = Array(repeating: 0, count: primesLength)
        
        primes[0] = 2
        primes[1] = 3
        primes[2] = 5
        primes[3] = 7
        primes[4] = 11
        primes[5] = 13
                
        var candidate = 17
        var firstEmptyIndex = 6
        
        while primes.last == 0 {
            var index = 1
            
            var isPrime = true
            var factor = primes[index]
            while isPrime && (factor * factor <= candidate) {
                if candidate % factor == 0 {
                    isPrime = false
                }
                index += 1
                factor = primes[index]
            }
            
            if isPrime {
                primes[firstEmptyIndex] = candidate
                firstEmptyIndex += 1
            }
            
            candidate += (form_6k_pm1 ? 4 : 2)
            form_6k_pm1.toggle()
        }
        
        print("The \(primesLength)th prime is \(String(describing: primes.last))")
        
        var brun = 0.0
        
        for i in 1..<primesLength {
            let twin1 = primes[i]
            let twin2 = primes[i-1]
            if twin1 == twin2 + 2 {
                brun += (1/Double(twin1)) + (1/Double(twin2))
            }
        }
        
        print(brun)
    }
}