From test case 2, it seems that you are asking for the closest prime number no less than n. Please clarify this ambiguity in the problem. Otherwise, the answer to test case 2 is 19 (not 23), which is the closest prime number to 20.
Final statement in problem statement disagrees with Case #1 of n=3.
I made a few quick edits.
I suggest to update this problem with big primes.
Is this matrix orthogonal?
Vectorize the digits of an Integer
Find the index of the largest value in any vector X=[4,3,4,5,9,12,0,4.....5]
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