Identify the incorrect number in the following series.
$$4,7,13,21,34$$

Let's analyze the differences between consecutive terms in the given series:
* $7-4=3$
* $13-7=6$
* $21-13=8$
* $34-21=13$

This sequence of differences ($3,6,8,13$) does not follow a clear pattern. Let's test a prime number difference pattern or consecutive multiples pattern:

If the differences were consecutive multiples of $3$ ($+3,+6,+9,+12$):

* First term: $4$
* Second term: $4+3=7$
* Third term: $7+6=13$
* Fourth term should be: $13+9=22$ (instead of $21$)
* Fifth term would be: $22+12=34$

This perfectly fits all the other numbers in the series except $21$. Therefore, $21$ is the wrong/incorrect number, and it should be replaced by $22$.