Let p, q, and c := (p + q)"q (where " denotes concatenation) be positive integers such that p and c are primes and q is the smallest prime such that c is prime.
Such a prime triple (p, q, (p + q)"q) is for example (9721, 101, 9822101).
In natural order, the results start 3, 7, 3, 3, 19, 3, 31, ...
Challenge
Write a function that, given p, returns q that satisfies the above conditions.
Make sure that the program can calculate the given example in a reasonable time (say in 99 seconds).
Rules
Standard I/O rules apply and no standard loopholes.
This is code-golf, so shortest code in bytes wins.
Postscript
This sequence has an interesting addition: if you run through the sequence and pick out a number as it first appears, you get a sequence that the author of A375552 conjectures to be a permutation of the prime numbers.