Given a number N. The task is to find the smallest special prime which is greater than or equal to N.
A special prime is a number which can be created by placing digits one after another such the all the resulting numbers are prime.
Input: N = 379 Output: 379 379 can be created as => 3 => 37 => 379 Here, all the numbers ie. 3, 37, 379 are prime. Input:N = 100 Output: 233
Approach: The idea is to use Sieve Of Eratosthenes. Build the sieve array up to the number N*10 (Assuming the number will exist in that range). Then start iteratively from the number N checking if the number is prime. If it is prime then check if it is special prime or not.
Now, to check if a number is a special prime or not. Keep dividing the number by 10 and at each point check whether the remaining number is prime or not, which we can do by referring our Sieve array which we have built.
Below is the implementation of the above approach:
- Find Largest Special Prime which is less than or equal to a given number
- Smallest number greater than or equal to N divisible by K
- Numbers with prime frequencies greater than or equal to k
- Kth prime number greater than N
- Check whether all the rotations of a given number is greater than or equal to the given number or not
- Smallest prime divisor of a number
- Smallest prime number missing in an array
- Check if the first and last digit of the smallest number forms a prime
- Smallest number k such that the product of digits of k is equal to n
- Sum of largest prime factor of each number less than equal to n
- Special prime numbers
- Smallest integer greater than n such that it consists of digit m exactly k times
- Longest subarray having average greater than or equal to x
- Next smallest prime palindrome
- Sum and product of k smallest and k largest prime numbers in the array