Task: Strong and weak primes




Go: package main

import "fmt"

func sieve(limit int) []bool {
    limit++
    
    
    c := make([]bool, limit)
    c[0] = true
    c[1] = true

    p := 3 
    for {
        p2 := p * p
        if p2 >= limit {
            break
        }
        for i := p2; i < limit; i += 2 * p {
            c[i] = true
        }
        for {
            p += 2
            if !c[p] {
                break
            }
        }
    }
    return c
}

func commatize(n int) string {
    s := fmt.Sprintf("%d", n)
    le := len(s)
    for i := le - 3; i >= 1; i -= 3 {
        s = s[0:i] + "," + s[i:]
    }
    return s
}

func main() {
    
    const limit = 1e7 + 19
    sieved := sieve(limit)
    
    var primes = []int{2}
    for i := 3; i <= limit; i += 2 {
        if !sieved[i] {
            primes = append(primes, i)
        }
    }
    
    var strong []int
    var weak = []int{3}                  
    for i := 2; i < len(primes)-1; i++ { 
        if primes[i] > (primes[i-1]+primes[i+1])/2 {
            strong = append(strong, primes[i])
        } else if primes[i] < (primes[i-1]+primes[i+1])/2 {
            weak = append(weak, primes[i])
        }
    }

    fmt.Println("The first 36 strong primes are:")
    fmt.Println(strong[:36])
    count := 0
    for _, p := range strong {
        if p >= 1e6 {
            break
        }
        count++
    }
    fmt.Println("\nThe number of strong primes below 1,000,000 is", commatize(count))
    fmt.Println("\nThe number of strong primes below 10,000,000 is", commatize(len(strong)))

    fmt.Println("\nThe first 37 weak primes are:")
    fmt.Println(weak[:37])
    count = 0
    for _, p := range weak {
        if p >= 1e6 {
            break
        }
        count++
    }
    fmt.Println("\nThe number of weak primes below 1,000,000 is", commatize(count))
    fmt.Println("\nThe number of weak primes below 10,000,000 is", commatize(len(weak)))
}




Python: import numpy as np

def primesfrom2to(n):
    
    
    sieve = np.ones(n//3 + (n%6==2), dtype=np.bool)
    sieve[0] = False
    for i in range(int(n**0.5)//3+1):
        if sieve[i]:
            k=3*i+1|1
            sieve[      ((k*k)//3)      ::2*k] = False
            sieve[(k*k+4*k-2*k*(i&1))//3::2*k] = False
    return np.r_[2,3,((3*np.nonzero(sieve)[0]+1)|1)]

p = primes10m   = primesfrom2to(10_000_000)
s = strong10m   = [t for s, t, u in zip(p, p[1:], p[2:]) 
                   if t > (s + u) / 2]
w = weak10m     = [t for s, t, u in zip(p, p[1:], p[2:]) 
                   if t < (s + u) / 2]
b = balanced10m = [t for s, t, u in zip(p, p[1:], p[2:]) 
                   if t == (s + u) / 2]

print('The first   36   strong primes:', s[:36])
print('The   count   of the strong primes below   1,000,000:',
      sum(1 for p in s if p < 1_000_000))
print('The   count   of the strong primes below  10,000,000:', len(s))
print('\nThe first   37   weak primes:', w[:37])
print('The   count   of the weak   primes below   1,000,000:',
      sum(1 for p in w if p < 1_000_000))
print('The   count   of the weak   primes below  10,000,000:', len(w))
print('\n\nThe first   10 balanced primes:', b[:10])
print('The   count   of balanced   primes below   1,000,000:',
      sum(1 for p in b if p < 1_000_000))
print('The   count   of balanced   primes below  10,000,000:', len(b))
print('\nTOTAL primes below   1,000,000:',
      sum(1 for pr in p if pr < 1_000_000))
print('TOTAL primes below  10,000,000:', len(p))