unsigned prime_count( unsigned n ) __override
{
    assert( n > 0 );

    unsigned count = 0;
    unsigned d = 2;

    while ( n > 1 )
    {
        if ( n % d == 0 )
            ++ count;

        while ( n % d == 0 )
            n /= d;

        ++ d;
    }

    return count;
}