Finding The nth Prime such that the prime - 1 is divisible by n Problem
The goal is as the title says to find the \$n\$th prime such that \$\text{the prime}-1\$ is divisible by \$n\$.
Explanation
Here is an example so you understand the question, this is not necessarily the way it ought to be solved. It merely as a way to explain the question
given \$3\$ as an input we would first look at all the primes
 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 ...

Then we select the primes such that \$\text{the prime}-1\$ is divisible by \$n\$ (3 in this case)
 7 13 19 31 37 43 61 67 73 79 97 103 107 109 127 ...

We then select the \$n\$th term in this sequence
We would output \$19\$ for an input of \$3\$
Note
We can also think of this as the \$n\$th prime in the sequence \$\{1, n + 1, 2n + 1, 3n + 1 ...kn + 1\}\$ where \$k\$ is any natural number
Test Cases
  1 --&gt; 2
  2 --&gt; 5
  3 --&gt; 19
  4 --&gt; 29
100 --&gt; 39301
123 --&gt; 102337
05AB1E, 9 8 bytes

05AB1E uses CP-1252 encoding.

Saved a byte thanks to Osable

µN¹*&gt;Dp½


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Explanation

µ          # for N in [1 ...] loop until counter == input
 N¹*&gt;      # N*input+1 (generate multiples of input and increment)
     D     # duplicate
      p½   # if prime, increase counter
           # implicitly output last prime