Finding a prime number after a given number

algorithm primes
avd picture avd · Mar 18, 2010 · Viewed 57.2k times · Source

How can I find the least prime number greater than a given number? For example, given 4, I need 5; given 7, I need 11.

I would like to know some ideas on best algorithms to do this. One method that I thought of was generate primes numbers through the Sieve of Eratosthenes, and then find the prime after the given number.

Answer

Rajendra Uppal picture Rajendra Uppal · Mar 18, 2010

Source: Wikipedia

Bertrand's postulate (actually a theorem) states that if n > 3 is an integer, then there always exists at least one prime number p with n < p < 2n − 2. A weaker but more elegant formulation is: for every n > 1 there is always at least one prime p such that n < p < 2n.

So if I am given a number, say n, than I can check in the range (n, 2*n) [open interval excluding n and 2*n]

int GetNextPrime(int n)
{
    bool isPrime = false;
    for (int i = n; i < 2 * n; ++i)
    {
    // go with your regular prime checking routine
    // as soon as you find a prime, break this for loop
    }
}

Related questions

Printing prime numbers from 1 through 100

This c++ code prints out the following prime numbers: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97. But I don't think that's the way my book wants it to be written. It mentions something about square root of a number. So I did try changing my 2nd loop …

Read More
Which is the fastest algorithm to find prime numbers?

Which is the fastest algorithm to find out prime numbers using C++? I have used sieve's algorithm but I still want it to be faster!

Read More
How to create the most compact mapping n → isprime(n) up to a limit N?

Naturally, for bool isprime(number) there would be a data structure I could query. I define the best algorithm, to be the algorithm that produces a data structure with lowest memory consumption for the range (1, N], where N is a …

Read More