The x585 requires BM19782 ( i have one for sale right now, PM me if still searching/interested)
JD Parts Catalog refers to your 4100's hitch as part # BM20921
Catalog "where used" search showed the following for BM20921:
Catalog Search Results
1926 - 47-Inch 2-Stage Snow Blower - 30Jun15 ( FR DE IT ES SV )
1936 - 54-Inch Front-Mounted Blade - 22Oct15
1937 - 46-Inch Snow Thrower - 23Oct15 ( FR DE IT ES SV )
2082 - 26, 246, 60 and 51-Inch Rotary Brooms - 22Oct15
9481 - 52-Inch and 60-Inch Rotary Brooms - 21Sep15 ( FR DE IT ES SV )
9501 - 2305 Compact Utility Tractor - 24Oct15 ( FR DE IT ES SV )
10426 - 54-Inch Snow Blower for 2305, 2320, 2520, 2720 Compact Utility Tractors - 19Dec14 ( FR DE IT ES SV )
If you need additional insights into the PTO shaft kit required for the X585 let me know - there 2WD and 4WD options. I just sold P/N AM132900 4WD PTO shaft online