Given a number N. The task is to find the largest special prime which is less 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 Explanation: 379 can be created as => 3 => 37 => 379 Here, all the numbers ie. 3, 37, 379 are prime. Input : N = 100 Output : 79 Explanation: 79 can be created as => 7 => 79, where both 7, 79 are prime numbers.
Approach: The idea is to use Sieve Of eratosthenes. Build the sieve array up to the number N. Then start iteratively back 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:
Time Complexity: O(N*log(log N))
- Smallest Special Prime which is greater than or equal to a given number
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- Sum of largest divisible powers of p (a prime number) in a range
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- Largest proper fraction with sum of numerator and denominator equal to a given number
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