Danger: Timewaster ahead

Steven found a nice set of Flash puzzles. Some are easy; others are trickier and require finesse to solve. Don’t click on the link unless you have at least a half-hour to spare.

By the way, you have four days left to figure out this year’s little number puzzle while it’s still timely. What is the next number in this sequence? It’s not 71.

23
27
31
39
43
47
55
59
63

(This is the American version. In other countries, the sequence is:

23
39
55
27
43
59
31
47
63

The solution is the same as for the American version.)