Different ways of defining primes One of my favorite definitions of the prime numbers goes as follows:


2 is the smallest prime.
Numbers larger than 2 are prime if they are not divisible by a smaller prime.


However this definition seems arbitrary, why 2?  Why not some other number?
Well lets try some other numbers will define n-prime such that


n is the smallest n-prime.
Numbers larger than n are n-prime if they are not divisible by a smaller n-prime.


Task

The task here is to write a program that takes two inputs, a positive integer n and a positive integer a.  It will then decide if a is n-prime.
Your program should output two distinct values one for "yes, it is n-prime" and one for "no, it is not n-prime".

This is a code-golf question so answers will be scored in bytes with less bytes being better.

Tests

Here are lists of the first 31 primes for n=2 to n=12 (1 is the only 1-prime number)

n=2: [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127]
n=3: [3,4,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127]
n=4: [4,5,6,7,9,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113]
n=5: [5,6,7,8,9,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113]
n=6: [6,7,8,9,10,11,13,15,17,19,23,25,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107]
n=7: [7,8,9,10,11,12,13,15,17,19,23,25,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107]
n=8: [8,9,10,11,12,13,14,15,17,19,21,23,25,29,31,35,37,41,43,47,49,53,59,61,67,71,73,79,83,89,97]
n=9: [9,10,11,12,13,14,15,16,17,19,21,23,25,29,31,35,37,41,43,47,49,53,59,61,67,71,73,79,83,89,97]
n=10: [10,11,12,13,14,15,16,17,18,19,21,23,25,27,29,31,35,37,41,43,47,49,53,59,61,67,71,73,79,83,89]
n=11: [11,12,13,14,15,16,17,18,19,20,21,23,25,27,29,31,35,37,41,43,47,49,53,59,61,67,71,73,79,83,89]
n=12: [12,13,14,15,16,17,18,19,20,21,22,23,25,27,29,31,33,35,37,41,43,47,49,53,55,59,61,67,71,73,77]
Haskell, 45 bytes



n!a=not$any(n!)[x|x&lt;-[n..a-1],mod a x&lt;1]||n&gt;a


Try it online!

I define a nice recursive function (!):

n!a checks if any factor of a, in the range [n,a-1], is an n-prime. Then it negates the result. It also makes sure that n&gt;a