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### by Sumit Chourasia | Oct 02, 2020 | Category :coding | Tags : algorithmdata-structureeasyleetcodemaths #### Prime Arrangements - Math - Easy - LeetCode

Return the number of permutations of 1 to n so that prime numbers are at prime indices (1-indexed.)

(Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.)

Since the answer may be large, return the answer modulo 10^9 + 7.

Example 1:

Input: n = 5
Output: 12
Explanation: For example [1,2,5,4,3] is a valid permutation, but [5,2,3,4,1] is not because the prime number 5 is at index 1.
Example 2:

Input: n = 100
Output: 682289015

Constraints:

1 <= n <= 100

``````public class Solution {
public int NumPrimeArrangements(int n) {
int mod = (int)Math.Pow(10, 9) + 7;
int count = 0;
for (int i = 2; i <= n; i++){
if (IsPrime(i)){
count++;
}
}

long res = 1;
for (int i = count; i > 0; i--)
{
res = (res * i) % mod;
res %= mod;
}

for (int i = n - count; i > 0; i--)
{
res = (res * i) % mod;
res %= mod;
}

return (int)res;
}

bool IsPrime(int num)
{
for (int i = 2; i <= num / 2; i++){
if (num % i == 0){
return false;
}
}

return true;
}
}``````

Time Complexity: O(n^2)

Space Complexity: O(1)