Primes: prime number in which (x, y) section

Also known prime number of prime numbers: a natural number larger than 1, except 1 and itself, the other can not be called a natural number divisible prime number;

 

The number of numbers is infinite. Euclid 's " Elements of geometry " in a classic proof. It uses a common method of proof: reductio ad absurdum . Specific demonstrated as follows: Suppose primes only limited n number, from small to large in order of priority of P _{. 1} , P ₂ , ......, P _n , set N = P _{. 1} × P ₂ × ...... × P _n , then, is a prime number or It is not a prime number. If a prime number is greater than P _{. 1} , P ₂ , ......, P _n- , so it is not a prime number of those hypothetical set.

 

Programming ideas: 1, a first determined number is not a prime number

               2, then prime numbers traverse (x, y) section to be listed

def isprime (n):

for i in range(2,n):
if n % i == 0 :
return False
else :
return True

print(isprime(7))

# Result: True

def prime_n2m (n,m):
L =[]
for x in range(n,m):
if isprime(x) == True :
L.append(x)
return L

print(prime_n2m(10,20))

# Results: [11, 13, 15, 17, 19]