Your Remington model 341-P was made from 1936-1940,with a total production of 131,604 made during this time span.The Remington society has the Date codes available for you to look up.Your barrel should have a 2,or 3 letter code that will give you the exact month and year of production.
I added the related link
Remington Model 552 Speedmaster
1914
The Remington Model 29 Pump Action shotgun was manufactured from 1930 to 1933. Approximately 38,000 produced.
I BELEIVE YOU HAVE A MODEL 241. IS THIS RIGHT??
1920
Manufactured 1927
1927
Made in 1911
Made 1912
1920
Impossible to answer without the sn.
Check the manufactured date link on the Remington Society of America for details.