Wow, thank you so much for the swift and efficient response!
That the highest recorded number is 628585 relieves me greatly as I could not understand why so many were quoting the 617*** range.
There is also a nice picture of a pistol in the Collectors Grade publication publication which again has a S/R beyond 617***.
Provenance of the pistol to the Chief Constable of the Royal Ulster Constabulary, Sir John "Jack" Herman, 1980-1989 was provided to me from the gun dealer in County Antrim where the firearm was sold, and, most importantly, I have the Chief Constable's Firearms Certificate, which of course has the Mauser M34 on it. For someone such as myself who has a small Mauser collection in Northern Ireland, this pistol represents a real piece of living history and acquiring it was a real scoop!