If Nicholas van Bergen graduated from Annapolis in 1921 (as suggested by Canadian Girls Scout's source) then it is possible that 1360 is his full Service Number.
The numbers 501 to 999 were issued to officers serving post WWI and from 1920 to the outbreak of WWII, numbers issued were from 1,000 to 125,000 (as the Navy grew rapidly).
Since he was born in 1900, graduating in the Class of 21 is feasible and so he could have a four digit number.
**Update:** It appears that _Bureau of Naval Personnel Information Bulletin No. 305 (August 1942)_ contains the citation for his Navy Cross. I would be very surprised if that did not provide corroboration of his Service Number,