According to the Remington site, the Model 580 was a single shot, the 581 took a magazine and the 582 was tubular feed. There is no reference to a Model 583. I have the Model 581 and 582. Good find, Joe. All the best...
Gil
http://www.remington.com/library/his...irearm_models/
Model 580
Description: Bolt Action, Single Shot
Introduction Year: 1967
Year Discontinued: 1987
Total Production: Approximately: 60,000
Designer/Inventor: Research & Development
Action Type: Bolt Action
Caliber/Gauge: .22 short, .22 long, .22 long rifle
Serial Number Blocks: Starting: N/A
Ending: N/A
# of Grades Offered: N/A
Variations