Can you generate the next number in this integer series and describe the rule?

2, 3, 5, 7, ... 11, 13, 17, ... 25, 29, ... 35, ... 43, 47, 49, ... 53, 59, 61, 65, 67, ... 71, ... ??

1. The answer (indicated by two question marks) has two digits.


2. When you see '...', it means that one or more numbers are deliberately concealed at that point.


3. The question is purely mathematical and some arithmetical calculation is needed.


4. The numbers always increase as you move from left to right. The mathematical term for this is that the sequence is monotonically increasing.

Hint 0

A member submitted the following comment:

Under the assumption that 2 is the only even number in the sequence, we can say that the first "..." is 9, the fifth is 51, and the sixth is 69.
That statement is false and, in order to solve the puzzle as intended, you must understand why.

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Hint 1

Ask yourself why there are gaps. What am I hiding?

Hint 2

It is an infinite sequence of integers, and 2 is the only even integer in the sequence.

Answer

The list contains:

the prime numbers in hexadecimal representation

The list then starts as:

2, 3, 5, 7, B, D, 11, 13, 17, 1D, 1F, 25, 29, 2B, 2F, 35, 3B, 3D, 43, 47, 49, 4F,

53, 59, 61, 65, 67, 6B, 6D, 71, 7F, 83, 89, 8B, 95, 97, 9D, A3, $\ldots,$ $\ldots,$ $\ldots$

Answer :

The answer to the puzzle is 83, the next term in the sequence given in the problem statement whose hexadecimal representation consists of two decimal digits.