pto100 = [
    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
    43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
]


def in_100(x):
    """Check if x is in the primes less than 100 i.e., in the first 25 primes.
    Useful for e.g. the first step in Baillie–PSW.
    """
    return x in pto100


def hund_div(x):
    """Check if x is divisible by any of the 25 primes less than 100. Returns 0
    if there is no such divisor, otherwise returns the first divisor.
    """
    for v in pto100:
        if v >= x:
            return 0
        if x % v == 0:
            return v
    return 0


def trd(x):
    """Express x as 2^r * d. Returns two values, r and d.
    """
    count = 0
    xc = x
    while xc % 2 == 0:
        count = count + 1
        xc = xc // 2
    return count, xc