It is tempting to think that the number 2 should be the designated driver for the whole endeavour:
2,3,5
2
2,7,11
2
2,13,17
2
2,19,23
which would take a total of 62 minutes. However we can get it under an hour:
2,3,5
2
7,11,13
3
17,19,23
5
2,3,5
which takes just 56 minutes.
But even this isn’t optimal. If we combine the two methods we can shave another minute off:
2,3,7
2
2,11,13
2
17,19,23
3
2,3,5
Giving a total of 55 minutes.