Explanation:

Correct option:4

Given series: 2, 5, 13, 29, ?

The logic followed here is:
• The prime numbers are missing between two prime numbers.
• One prime number is missing between 2 and 5 then, two prime numbers are missing between 5 and 13, and so on. 

2          5           13                  29                     47
    (3)      (7,11)      (17,19,23)      (31,37,41,43)

The pattern followed is: 2 (3) 5 (7 11) 13 (17 19 23) 29 (31 37 41 43) 47

Hence, the correct answer will be 47.