import gmpy2
from gmpy2 import mpz, next_prime
from multiprocessing import Pool, cpu_count

def int_to_base_n(num, base):
    if num == 0:
        return '0'
    digits = ''
    while num > 0:
        rem = num % base
        if rem < 10:
            digits = str(rem) + digits
        else:
            digits = chr(ord('A') + rem - 10) + digits
        num //= base
    return digits

def find_prime_index(n_base_tuple):
    n, base = n_base_tuple
    num_str = int_to_base_n(n, base)
    current_prime = mpz(2)
    index = 1
    num_length = len(num_str)
    while True:
        prime_str = int_to_base_n(int(current_prime), base)
        if num_str in prime_str:
            return index
        current_prime = next_prime(current_prime)
        index += 1
        while len(int_to_base_n(int(current_prime), base)) < num_length:
            current_prime = next_prime(current_prime)
            index += 1

def positive_integer_prime_sequence(limit, base):
    n_values = list(range(1, limit + 1))
    n_base_tuples = [(n, base) for n in n_values]
    num_processes = min(len(n_values), cpu_count())
    with Pool(processes=num_processes) as pool:
        sequence = pool.map(find_prime_index, n_base_tuples)
    return sequence

if __name__ == "__main__":
    N = 1000  # number of terms in sequence
    base = 2  # base in which numbers are represented
    print(','.join(map(str, positive_integer_prime_sequence(N, base))))