#!/usr/bin/env python
from random import randrange as rndrng
from primelist import primeList
fpl = primeList(10000)
def nBR(n):
    return rndrng(2**(n-1)+1, 2**n-1)
def gLLP(n):
    while True:
        pc = nBR(n)
        for d in fpl:
            if pc % d == 0 and d**2 <= pc:
                break
            else: return pc
def iMRP(mrc):
    mDBT = 0
    ec = mrc-1
    while ec % 2 == 0:
        ec >>= 1
        mDBT += 1
    assert(2**mDBT * ec == mrc -1)
    def tC(rt):
        if pow(rc, ec, mrc) == 1:
            return False
        for i in range(mDBT):
            if pow(rc, 2**i * ec, mrc) == mrc-1:
                return False
        return True
    nORT = 20
    for i in range(nORT):
        rc = rndrng(2, mrc)
        if tC(rc):
            return False
        return True
def genPrime():
    while True:
        n = 512
        pc = gLLP(n)
        if not iMRP(pc):
            continue
        else:
            return pc