The 7 or 8 digits-long number at the top is as follows:
If it's 7 digits, the first digit identifies the die. If it's 8 digits, the die number is the first two digits.
Second 2 digit group is the operator ID (often left to 00)
Third 2 digit group is tester or inspector (not sure, also often left to 0)
Fourth 2 digit group is year of production. \
So 34000013 is die 34, operator and inspector not identified, made in 2013. Edit: this just so happens to be the one that Simon is lusting after. ;-)
The Filthy Pig
: Air Arms 100 (1990) + AA Olympic trigger + Welham reg + Custom Shop CS1000 stock. Status: leaking.
The Unknown Quantity
: AA EV2 Mk4. + BSA Platinum 10-50x60 + Jon Harris wheel. Status: sorted up to 25 yds.
The Limping Dog
: Air Arms Shamal (1989) + unknown origin sporter stock + Optisan Cobra 3-9x42. Status: slowly leaking; needs work.
: HW97k + Venom Lazaglide. Status: working just fine; needs scope.
with apologies to NJR100