Given a positive integer N where . The task is to find the smallest prime palindrome greater than or equal to N.
Input: 8 Output: 11 Input: 7000000000 Output: 10000500001
The Naive approach is to loop from N + 1 until we found next smallest prime palindrome greater than or equal to N.
Lets say P = R is a the next smallest prime-palindrome greater than or equal to N.
Now since R is a palindrome, the first half of the digits of R can be used to determine R up-to two possibilities. Let k be the first half of the digits in R. For eg. if k = 123, then R = 12321 or R = 123321.
Thus we iterate through each k upto 105 and create the associated palindrome R, and check whether R is a prime or not.
Also we will handle the odd and even palindromes separately, and break when we fount our result.
Below is the implementation of above approach:
Time Complexity: O(N*sqrt(N)) where N is upper limit and the sqrt(N) term comes from checking if a candidate is prime.
- Find next palindrome prime
- Given a number, find the next smallest palindrome
- Smallest and Largest Palindrome with N Digits
- Construct lexicographically smallest palindrome
- Make a lexicographically smallest palindrome with minimal changes
- Make lexicographically smallest palindrome by substituting missing characters
- Smallest prime divisor of a number
- Smallest prime number missing in an array
- Smallest Special Prime which is greater than or equal to a given number
- Check if the first and last digit of the smallest number forms a prime
- Sum and product of k smallest and k largest prime numbers in the array
- Queries for the smallest and the largest prime number of given digit
- Sentence Palindrome (Palindrome after removing spaces, dots, .. etc)
- Count all palindrome which is square of a palindrome
- Count occurrences of a prime number in the prime factorization of every element from the given range
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