素数任务

Question

Hi I have task that that I dont know how to do. Basically I need to write primal numberswhere is only difference by 2 numbers, only primal number which is either two more or two less than another prime number and then print every pair of these primes that are less than or equal to 100. Here is how it should look like.

3 5

5 7

11 13

17 19

29 31

41 43

59 61

71 73

Here is my code.I don't know how to eliminate these that are more than 2

for b in range(1, n):      
  if b>2:                    
      for p in range(2, b):  
         if (b%p) ==0:
          break
      else: 
        print(b )

Answer 1

Without changing your existing code, you could do:

    lastprime = 2
    for b in range(1, n):      
      if b>2:                    
          for p in range(2, b):  
             if (b%p) ==0:
              break
          else:
            if b == lastprime + 2:
                print(lastprime, b)
            lastprime = b

Answer 2

It should be a bit more efficient by using Sieve of Eratosthenes:

sieve = [True for _ in range(n + 1)]
current_number = 2
while (current_number * current_number <= n):
    if (sieve[current_number] == True):
        for i in range(current_number * current_number, n + 1, current_number):
            sieve[i] = False
    current_number += 1

primes = [index for index in range(2, n + 1) if sieve[index]]
for i in range(len(primes) - 1):
    first = primes[i]
    second = primes[i + 1]
    if first + 2 == second:
        print(f'{first} {second}')

or even more efficient:

sieve = [False] * 2 + [True] * (n - 1)
for number in range(int(n ** 0.5 + 1.5)):
    if sieve[number]:
        for i in range(number * number, n + 1, number):
            sieve[i] = False
primes = [i for i, prime in enumerate(sieve) if prime]
for i, first in enumerate(primes[:-1]):
    second = primes[i + 1]
    if first + 2 == second:
        print(f'{first} {second}')

Explanation:
https://www.geeksforgeeks.org/sieve-of-eratosthenes/