As discussed in the rare variants thread, a factory cutaway Glock is a very limited production specimen. The very first made were AT prefix Gen 1 Glock 17s, first cut by one of the machinists at the factory, who decided to cut a production gun and see if they could make a working model for sales demonstrations. Gaston Glock saw it and loved the idea so he set aside the JQ prefix as a designated Cutaway serial bank. The latest model I’ve seen of current production is in the JQ4000 serial range so there have been less than 5,000 total cutaways made across 35 years combined through all generations and models. These were only sold to Law Enforcement or certified Glock armorers for demonstration and training purposes. A few were also carried by early Glock sales reps to demonstrate the internal safeties–which were a concern for police in the early days.
The rarity of cutaway models increases significantly the further back in history you go. The only Gen 1s made were model 17s and there were fewer than 200 total made (as evidenced by my Gen 2 bearing serial JQ200). The Gen 2 total run was less than 1,000 guns across models 17, 19, 20, 21, 22, and 23. Thus far, I have not been able to find a definite range of transition between 2s and 3s though it was above JQ800 and below JQ1200. The Gen 3s and 4s are still being made simultaneously but in limited numbers. I’ve also heard of Gen 5s but have yet to see any real life specimens.
Here is a selection of cutaways from my personal collection:
A Brief History of Glock Firearms Aimed at Collectors 