The numbers 2 and 3 are both prime, so both have two factors, themselves and 1.
While there are no other examples of consecutive primes, it’s not difficult to find more pairs of consecutive integers with the same number of factors:
Eventually you get to sets of three consecutive integers with the same number of factors:
33 
34 
35 
11 
17 
7 
3 
2 
5 
1 
1 
1 
 
85 
86 
87 
17 
43 
29 
5 
2 
3 
1 
1 
1 

It isn’t possible to have a sequence of more than three integers with only four factors, but so far I have found this set of four consecutive integers with six factors:
242 
243 
244 
245 
121 
81 
122 
49 
22 
27 
61 
35 
11 
9 
4 
7 
2 
3 
2 
5 
1 
1 
1 
1 
I’m sure that somewhere out there I can find out whether or not a) there are longer sequences of consecutive integers which the same number of factors and b) whether there is a natural limit to the process. That’s as far as I can take it in the sleepless hours of the night though.
Related
I suspect the answer to all these sorts of questions depends on who I am with, the formality of the speech, how much I’ve had to drink and many other factors.