pseudocode.pc

const k, n, b, c;  # they have to have values
const N = k * b ^ n - 1;

# find V1
# this uses Jacobi Symbols
while (v1 := 1) : () : (v1 += 1) {
    if jacobi(v1 - 2, N) == 1 && jacobi(v1 + 2, N) == -1 {
        break
    }
}

# fastest method [ O(log(bitlen(k))) ] to find u0
# this calculates the value of the Lucas Sequence
x = v1
y = (v1 * v1) - 2
k_bitlen = bitlen(k)
while (i := k_bitlen - 2) : (i > 0) : (i -= 1) {
    if k.bits[i] == 1 {
        x = (x*y) - v1 mod N
        y = (y*y) - 2 mod N
    } else {
        y = (x*y) - v1 mod N
        x = (x*x) - 2 mod N
    }
}
x = x * x
x = x - v1
u = u0 = x mod N

# Lucas-Lehmer-Riesel primality test starting from U0
while (i := 1) : (i < n - 1) : (i += 1) {
    u = (u * u) - 2
}
'prime!' if u == 0