Prime number. Using Functions. Using LIST Comprehension.

Exercise11.py

####################### 
#   Using Functions: 
#######################

def get_number(prompt):
	return int(input(prompt))

def is_prime(number):
	if number == 1:
		prime = False
	elif number == 2:
		prime = True
	else:
		prime = True
		for i in range(2,number):
			if number % i == 0:
				prime = False
				break
	return prime

def print_prime(number):
	prime = is_prime(number)
	if prime:
		desc = ""
	else:
		desc = "not"
	print(number,"is",desc,"a prime number!")

while 1==1:
	print_prime(get_number("Enter a number: "))

###########################################
#		Using List Comprehension:
###########################################

''' This solution doesn’t use functions, but does use list comprehensions, which are always fun.
	Thanks to Carlos for this solution.
	The interesting thing here is the observation that when you want to check if a number is prime, 
	all you need to do is check the numbers from 2 to the square root of the number.
	This is because the pair of numbers that are both the largest factors of the number are square root of x and square root of x.
	Otherwise, the number you are checking for can be found by finding the corresponding factor and checking it.
'''
			######## NOT a bit can I understand here. ##########

# Assumes that "a" contains an integer > 2 whose primality needs to be verified
# The algorithm builds a list of factors including the number 2 and all odd numbers 
# up to the square root of "a", and then checks if any of those numbers divides "a" 
# without a remainder - if so then "a" is not prime, else it is

if sum([ True if a%factor == 0 else False for factor in ( [2] + list(range(3,int(math.sqrt(a)),2) )) ]): 
  print("Number is composite")
else: 
  print("Number is prime")


#################################################
#  Using List Comprehension (simpler one)
#################################################

num = int(input("Enter a number: "))
a =[x for x in range(2,num) if num % x == 0]
def is_prime(n):
	if num > 1:
		if len(a) == 0:
			print("Prime")
		else:
			print("Not Prime.")
	else:
		print("Not prime.")
is_prime(num)


a =int(input("Enter first:"))
b =int(input("Enter second:"))
for number in range(a,b+1):
	for num in range(2,a):
		if number % num == 0:
			break
	else:
		print(number, end=" ")