Two sequences with more than one logic

Question

Find the missing terms in the sequences below

5, 7, 11, 15,...?

A) 23
B) 28
C) 25
D) 19

10, 11, 19, 23, ?, 41...

A) 24
B) 28
C) 31
D) 37

Interestingly, the exercise presents alternatives. I believe that to force the identification of a specific logic. The first sequence appears to be equal to the number of unrestricted partitions of $n \; (a_n = p (n + 4), n \geq 0)$. Thus, the term that should follow 15 should be 22, which is not present in the alternatives.

The second sequence differs from this by only one term (the desired one). I can't capture the difference between the two

Source: Handbook of Codes and Sequences with Applications in Communication, Computing and Information Security (Discrete Mathematics and Its Applications)

Answer 1

Partial answer

First sequence

If $p_n$ are the prime numbers then this sequence is given by $2p_n+1$ so the next element of the sequence is 23.

Answer 2

Second sequence:

37

Because with the prime number sequence you have 2x3+4, 3x3+2, 5x3+4, 7x3+2, 11x3+4, 13x3+2 etc.