Smallest Special Prime which is greater than or equal to a given number

• Last Updated : 23 Nov, 2021

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.
Examples:

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:

C++

 // CPP program to find the Smallest Special Prime// which is greater than or equal to a given number#include using namespace std; // Function to check whether the number// is a special prime or notbool checkSpecialPrime(bool* sieve, int num){    // While number is not equal to zero    while (num) {        // If the number is not prime        // return false.        if (!sieve[num]) {            return false;        }         // Else remove the last digit        // by dividing the number by 10.        num /= 10;    }     // If the number has become zero    // then the number is special prime,    // hence return true    return true;} // Function to find the Smallest Special Prime// which is greater than or equal to a given numbervoid findSpecialPrime(int N){    bool sieve[N*10];     // Initially all numbers are considered Primes.    memset(sieve, true, sizeof(sieve));    sieve = sieve = false;    for (long long i = 2; i <= N*10; i++) {        if (sieve[i]) {             for (long long j = i * i; j <= N*10; j += i) {                sieve[j] = false;            }        }    }     // There is always an answer possible    while (true) {        // Checking if the number is a        // special prime or not        if (checkSpecialPrime(sieve, N)) {            // If yes print the number            // and break the loop.            cout << N << '\n';            break;        }        // Else increment the number.        else            N++;    }} // Driver codeint main(){    int N = 379;     findSpecialPrime(N);     N = 100;    findSpecialPrime(N);     return 0;}

Java

 // Java program to find the Smallest Special Prime// which is greater than or equal to a given number class GFG{     // Function to check whether the number// is a special prime or notstatic boolean checkSpecialPrime(boolean []sieve, int num){    // While number is not equal to zero    while (num > 0)    {        // If the number is not prime        // return false.        if (sieve[num])        {            return false;        }         // Else remove the last digit        // by dividing the number by 10.        num /= 10;    }     // If the number has become zero    // then the number is special prime,    // hence return true    return true;} // Function to find the Smallest Special Prime// which is greater than or equal to a given numberstatic void findSpecialPrime(int N){    boolean[] sieve = new boolean[N * 10 + 1];     // Initially all numbers are considered Primes.    sieve = sieve = true;    for (int i = 2; i <= N * 10; i++)    {        if (!sieve[i])        {            for (int j = i * i; j <= N * 10; j += i)            {                sieve[j] = true;            }        }    }     // There is always an answer possible    while (true)    {        // Checking if the number is a        // special prime or not        if (checkSpecialPrime(sieve, N))        {            // If yes print the number            // and break the loop.            System.out.println(N);            break;        }                 // Else increment the number.        else            N++;    }} // Driver codepublic static void main(String[] args){    int N = 379;     findSpecialPrime(N);     N = 100;    findSpecialPrime(N);}} // This code contributed by Rajput-Ji

Python3

 # Python 3 program to find the Smallest# Special Prime which is greater than or# equal to a given number # Function to check whether the number# is a special prime or notdef checkSpecialPrime(sieve, num):         # While number is not equal to zero    while (num):                 # If the number is not prime        # return false.        if (sieve[num] == False):            return False         # Else remove the last digit        # by dividing the number by 10.        num = int(num / 10)     # If the number has become zero    # then the number is special prime,    # hence return true    return True # Function to find the Smallest Special# Prime which is greater than or equal# to a given numberdef findSpecialPrime(N):    sieve = [True for i in range(N * 10 + 1)]     sieve = False    sieve = False     # sieve for finding the Primes    for i in range(2, N * 10 + 1):        if (sieve[i]):            for j in range(i * i, N * 10 + 1, i):                sieve[j] = False         # There is always an answer possible    while (True):                 # Checking if the number is a        # special prime or not        if (checkSpecialPrime(sieve, N)):                         # If yes print the number            # and break the loop.            print(N)            break             # Else increment the number.        else:            N += 1 # Driver codeif __name__ == '__main__':    N = 379     findSpecialPrime(N)     N = 100    findSpecialPrime(N) # This code is contributed by# Surendra_Gangwar

C#

 // C# program to find the Smallest Special Prime// which is greater than or equal to a given numberusing System; class GFG{     // Function to check whether the number// is a special prime or notstatic bool checkSpecialPrime(bool []sieve, int num){    // While number is not equal to zero    while (num > 0)    {        // If the number is not prime        // return false.        if (sieve[num])        {            return false;        }         // Else remove the last digit        // by dividing the number by 10.        num /= 10;    }     // If the number has become zero    // then the number is special prime,    // hence return true    return true;} // Function to find the Smallest Special Prime// which is greater than or equal to a given numberstatic void findSpecialPrime(int N){    bool[] sieve = new bool[N * 10 + 1];     // Initially all numbers are considered Primes.    sieve = sieve = true;    for (int i = 2; i <= N * 10; i++)    {        if (!sieve[i])        {            for (int j = i * i; j <= N * 10; j += i)            {                sieve[j] = true;            }        }    }     // There is always an answer possible    while (true)    {        // Checking if the number is a        // special prime or not        if (checkSpecialPrime(sieve, N))        {            // If yes print the number            // and break the loop.            Console.WriteLine(N);            break;        }                 // Else increment the number.        else            N++;    }} // Driver codestatic void Main(){    int N = 379;     findSpecialPrime(N);     N = 100;    findSpecialPrime(N);}} // This code is contributed by mits



Javascript


Output:
379
233

My Personal Notes arrow_drop_up