# Python3 Program to Count Primes in Ranges

• Last Updated : 13 Jan, 2022

Given a range [L, R], we need to find the count of total numbers of prime numbers in the range [L, R] where 0 <= L <= R < 10000. Consider that there are a large number of queries for different ranges.
Examples:

```Input : Query 1 : L = 1, R = 10
Query 2 : L = 5, R = 10
Output : 4
2
Explanation
Primes in the range L = 1 to R = 10 are
{2, 3, 5, 7}. Therefore for query, answer
is 4 {2, 3, 5, 7}.
For the second query, answer is 2 {5, 7}.```

A simple solution is to do the following for every query [L, R]. Traverse from L to R, check if current number is prime. If yes, increment the count. Finally, return the count.
An efficient solution is to use Sieve of Eratosthenes to find all primes up to the given limit. Then we compute a prefix array to store counts till every value before limit. Once we have a prefix array, we can answer queries in O(1) time. We just need to return prefix[R] – prefix[L-1].

## Python3

 `# Python3 program to answer queries for ``# count of primes in given range.``MAX` `=` `10000`` ` `# prefix[i] is going to``# store count of primes``# till i (including i).``prefix ``=``[``0``]``*``(``MAX` `+` `1``)`` ` `def` `buildPrefix():``     ` `    ``# Create a boolean array value in``    ``# prime[i] will "prime[0..n]". A ``    ``# finally be false if i is Not a``    ``# prime, else true.``    ``prime ``=` `[``1``]``*``(``MAX` `+` `1``)`` ` `    ``p ``=` `2``    ``while``(p ``*` `p <``=` `MAX``): `` ` `        ``# If prime[p] is not changed, ``        ``# then it is a prime``        ``if` `(prime[p] ``=``=` `1``):`` ` `            ``# Update all multiples of p``            ``i ``=` `p ``*` `2``            ``while``(i <``=` `MAX``):``                ``prime[i] ``=` `0``                ``i ``+``=` `p``        ``p``+``=``1`` ` `    ``# Build prefix array``    ``# prefix[0] = prefix[1] = 0;``    ``for` `p ``in` `range``(``2``,``MAX``+``1``): ``        ``prefix[p] ``=` `prefix[p ``-` `1``]``        ``if` `(prime[p]``=``=``1``):``            ``prefix[p]``+``=``1`` ` `# Returns count of primes ``# in range from L to``# R (both inclusive).``def` `query(L, R):``    ``return` `prefix[R]``-``prefix[L ``-` `1``]`` ` `# Driver code``if` `__name__``=``=``'__main__'``:``    ``buildPrefix()`` ` `    ``L ``=` `5``    ``R ``=` `10``    ``print``(query(L, R))`` ` `    ``L ``=` `1``    ``R ``=` `10``    ``print``(query(L, R))`` ` `# This code is contributed by mits.`

Output:

```2
4```

Please refer complete article on Count Primes in Ranges for more details!

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