// MillerRabinK test if n is a prime, testing for k times.
func MillerRabinK(n int64, k int) bool {
if n <= 3 {
return n > 1
}
if n%2 == 0 {
return false
}
d := n - 1
s := 0
for d%2 == 0 {
d /= 2
s++
}
for ; k > 0; k-- {
x := number.ModularPower(rand.Int63n(n-3)+2, d, n)
if x == 1 || x == n-1 {
continue
}
r := 1
for ; r < s; r++ {
x = number.ModularMultiply(x, x, n)
if x == 1 {
return false
}
if x == n-1 {
break
}
}
if r == s {
return false
}
}
return true
}
// PollarRho returns a divisor of n.
func PollarRho(n int64) int64 {
if n%2 == 0 {
return 2
}
for {
x := rand.Int63n(n)
y := x
c := rand.Int63n(n)
for {
f := func(x int64) int64 {
return (number.ModularMultiply(x, x, n) + c) % n
}
x = f(x)
y = f(f(y))
d := number.GCD(abs(x-y), n)
if d == n {
break
}
if d > 1 {
return d
}
}
}
}