JuniorMath
Prime Arrangements
Return the number of permutations of 1 to n so that prime numbers are at prime indices, using 1-indexing.
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 = 5Output
12For 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 = 100Output
682289015There are 682289015 valid permutations modulo 10^9 + 7.
Constraints
- 1 <= n <= 100