Python-сообщество

 from math import sqrt
primes = [2]
for i in range(3, 32000, 2):
    isprime = True
    cap = sqrt(i) + 1
    for j in primes:
        if (j >= cap):
            break
        if (i % j == 0):
            isprime = False
            break
    if (isprime):
        primes.append(i)
T = int(input())
output = ""
for t in range(T):
    if (t > 0):
        output += "\n"
    M, N = (int(i) for i in input().split())
    M = int(M)
    N = int(N)
    cap = sqrt(N) + 1
    if (M < 2):
        M = 2
    isprime = [True] * 100001
    for i in primes:
        if (i >= cap):
            break
        if (i >= M):
            start = i * 2
        else:
            start = M + ((i - M % i) % i)  # вот здесь непонятно
        falseblock = [False] * len(isprime[start - M:N + 1 - M:i])  # и здесь тоже
        isprime[start - M:N + 1 - M:i] = falseblock  #
    for i in range(M, N + 1):
        if (isprime[i - M] == True):
            output += str(i) + "\n"
print(output[:-1])