Programming puzzle: Longest list of regular numbers?

[pier4r]

Description:
A regular number is a number that divides evenly a power of 60 (so at least one of the following numbers 60, 3600, 216000, \( 60^4 \) , \( 60^5 \) and so on)

Challenge #1:
Print on the screen all the regular numbers found in 120 seconds without gaps (so, without focusing on a subset of the regular numbers. One has to return consecutive regular numbers). If the program fails to produce any regular number after 120 seconds (unlikely, since the first is 2), one can just report the first regular number found and how much time was needed.
Note: No quick start allowed. One has to start from 2.

For example by hand using my el506w as support (or using the properties of regular numbers, those are faster to apply mentally) I can do this in 120 seconds:

2,3,4,5,6,8,9,10,12,15,16,18,20

Challenge #2 (longer):
Find the 1429th regular number, return the time needed for the computation (I'm not sure if this would stretch thin some old calculators).
Note: No quick start allowed. One has to start finding numbers from 2.

Challenge #2a (for very fast hw/solutions):
Like #2, but one has to find the 9733rd regular number. (for computers, one has the original challenge that raises the bar a bit)

Source of the idea.