20210112

58_spiral_primes/main.go

@@ -0,0 +1,69 @@
+package main
+
+import (
+	"errors"
+	"fmt"
+)
+
+func main() {
+	n := 26239
+	for {
+		fmt.Println(n)
+		nums, err := findSprialDiagonals(n)
+		if err != nil {
+			fmt.Println(err)
+			break
+		}
+		if primeRatio(nums) < 0.1 {
+			fmt.Println(n)
+			break
+		}
+		n += 2
+	}
+}
+
+func findSprialDiagonals(width int) ([]int, error) {
+	if width%2 == 0 {
+		return nil, errors.New("invalid width")
+	}
+	x := 3
+	ret := []int{1}
+	cw := 3
+	d := 2
+	for width/cw > 0 {
+		ret = append(ret, []int{x, x + d, x + 2*d, x + 3*d}...)
+		x = x + 3*d + cw + 1
+		cw += 2
+		d = cw - 1
+	}
+	return ret, nil
+}
+
+func primeRatio(nums []int) float64 {
+	pc := float64(0)
+	for _, n := range nums {
+		if isPrime(n) {
+			pc++
+		}
+	}
+	return pc / float64(len(nums))
+}
+
+func isPrime(n int) bool {
+	if n <= 1 {
+		return false
+	}
+	res := n
+	//牛顿法求平方根
+	for res*res > n {
+		res = (res + n/res) / 2
+	}
+	divider := 2
+	for divider <= res {
+		if n%divider == 0 {
+			return false
+		}
+		divider++
+	}
+	return true
+}