Question

Write a smallest_gap(start_num, end_num) function that finds smallest gap between successive primes, considering prime numbers in the range from start_num to end_num (inclusive).

For example, start_num = 5 and end_num = 12, the prime numbers in that range are: [5, 7, 11]. The smallest gap between any two prime numbers in this list is 2, so the function would return 2.

Some example test cases (include these test cases in your program):

>>> print(smallest_gap(5, 12))

2

# The primes between 1000 and 1020 are 1009, 1013, 1019 so the smallest gap

# is 4 as 1013 – 1009 = 4
>>> print(smallest_gap(1000,1020))
4

In PyCharm

Answer 1

def smallest_gap(start_num, end_num):
    lst = []
    for n in range(start_num, end_num + 1):
        is_prime = n > 1
        for i in range(2, n):
            if n % i == 0:
                is_prime = False
        if is_prime:
            lst.append(n)
    min_gap = None
    for i in range(1, len(lst)):
        if min_gap is None or lst[i] - lst[i - 1] < min_gap:
            min_gap = lst[i] - lst[i - 1]
    return min_gap


# Testing the function here. ignore/remove the code below if not required
print(smallest_gap(5, 12))
print(smallest_gap(1000, 1020))