1903 Year by Serial Number Help

[wayne7161976]

New to the site and vintage rifles. I recently was given what I believe is a 1903 Savage Pump 22. I would love it if some one could help with the year it was made. Serial number 31876.

[Sav22]

The closest I have dates for are 332xx, 6/23/1905, and 135xx, 5/18/1904. The first ones were April of 1903. Shoot only standard velocity or lighter ion these.