triangular_numbers.py

def tn(n):
    if n == 0:
        return 0
    else:
        return n + tn(n-1)

x = []
def cp(k):
    s = k
    i = 2
    while (k > 1):
        while(k % i == 0):
            x.append(i)
            k /= i
        i += 1
        if len(x) == 100:
            print(s)
            break
j = 1
while (j > 0):
    cp(tn(j))
    j += 1
def prime(num):
    """"
    To check whether a number is prime
    """
    num2 = num
    while num2 > 0:
        if num == num2: 
            num2 -= 1
        elif num2 == 1:
            num2 -= 1            
        elif num % num2 == 0:
            return False
        num2 -= 1
        
    return True

try:
    #defines the range within which the twin primes to be found
    n = int(input('Enter a number within which the twin primes are to be found: '))
    if n <= 3:
        raise ValueError
    rangeList = range(2,n) 
    #list of prime numbers is created using filter()
    primeList = list(filter(prime, rangeList))
    print('\n')
    
    print('There are {0} prime numbers from 1 to {1}. They are:' .format(len(primeList), n))
    print(primeList)
    
    print('\n')
    #using list comprehension to create a list of twin primes
    twinPrimes = [(i, i+2) for i in primeList if i+2 in primeList]
    print('There are {0} twin primes from 1 to {1}. They are:' .format(len(twinPrimes), n))
    print(twinPrimes)
    print('\n')
      
except(ValueError):
    print('Please enter a valid integer number greater than 3')