TITLE: Infinite 2-generated simple group
QUESTION [5 upvotes]: I am looking for a concrete example of an infinite simple group with two generators.  Ideally, one generator has order 2, the other 3, but if there is a nice example without this requirement, it will be appreciated.
Schupp proved that every countable group embeds into such a group, but I would like to see a concrete easy example (where it is easy to show simplicity).

REPLY [2 votes]: R. Thompson's group V is an infinite simple finitely presented group admitting a presentation with 2 generators and 7 relations (generator orders are 2 and 6 in our paper (arXiv:1511.02123) with Martyn Quick).  
The group V admits many generating sets, and I would not be surprised if you could find a generating pair having orders 2 and 3 respectively.