Figuring out whether a given number is prime, while not very complicated, is kind of hard. But making a guess doesn't need to be.

Seeing whether a number is a multiple of 2 or 5 is easy - you can just look at the last digit. Multiples of 3 isn't much harder, just add up the digits and see if you end up with a multiple of 3. Multiples of 11 are also easy enough, at least as long as they're fairly small. Any other number might not *be* prime, but at least they look like they *might* be prime. Or at least, that's how it works in base ten. As a person who frequently uses base ten, you can probably also identify the single-digit primes, and know that 11 is a prime as well.

We can generalize this to other bases. In some base \$b \ge 2\$, you can find fairly simple divisibility rules for any factor of \$b, b-1 \text{ or }b+1\$. You also presumably know all the prime numbers up to and including \$b+1\$.

But in any base, you eventually start running into numbers that *look* prime, but *aren't*. And I want to know when that happens. I know that in base 10, the first such number is 49 (not divisible by 2, 3, 5 or 11, but also not prime), in base 12 it's 25 (not divisible by 2, 3, 11 or 13), and in base 27, it's 55 (not divisible by 2, 3, 7 or 13, and unlike 25 it's also big enough to require two digits!). But for other bases? That's where you come in!

Rules
-----

Your task is to write a program or function which takes as input some integer \$b\ge2\$ and outputs the first integer which, when written in base \$b\$ *looks* like it might be prime, but *isn't*. That is to say, the smallest integer that

* Is a composite number and
* Is greater than \$b\$ and
* Is coprime with (does not share any prime factors with) \$b-1\$, \$b\$ and \$b+1\$

This is related to [OEIS A090092](https://oeis.org/A090092), but starts to diverge at \$b=27\$

This is [code-golf](/questions/tagged/code-golf "show questions tagged 'code-golf'"), so save those bytes!

Test cases
----------

```
Base -> Smallest pseudo-prime
2 -> 25
5 -> 49
6 -> 121
10 -> 49
12 -> 25
27 -> 55
32 -> 35
34 -> 169
37 -> 49
87 -> 91
88 -> 91
89 -> 91
121 -> 133
123 -> 125
209 -> 289

```