Question

Given a number n, what is the largest gap between successive primes which are less than number n?

For example, if n = 12, the prime numbers less than 12 are: [2, 3, 5, 7, 11]. The largest gap between any two prime numbers in this list is 4, so the function would return '4'. >>>print(largestGap(12))

4

Write Python code to solve this problem, and include the following 3 test cases in your answer.

>>>print(largestGap(100))

8

>>>print(largestGap(1000))

20

>>>print(largestGap(10000))

36

Answer 1

    
def largestGap(num):
    f_prime=0;"""to store the latest prime number"""
    s_prime=0;"""To store the previous prime number"""
    gap=0;"""to store the gap between two successive prime numbers"""
    for j in range(2,num):
        cnt=0;
        for i in range(2,j/2):
            if(j%i == 0):
                cnt=1;
                break;
        if(cnt == 0):
           s_prime=f_prime;
           f_prime=j;
           if(gap<f_prime-s_prime):
               gap=f_prime-s_prime;
    print(gap); 
    
largestGap(100);  

The j loop is to iterate from 2 till the number passed to the function.

i loop is to check if the number passed from j loop is prime or not.

it checks if the value of j is divisible by 2 till number/2.if divisible,breaks from the loop;

if not divisble by any number from 2 till number/2,its a prime.this value is assigned to f_prime and the previous number is assigned to s_prime.

then checks if gap is less than f_prime-s_prime. if yes gap is assigned this value.