Could a 400-calibre-length gun work?

Could a gun with a barrel roughly 400 calibres long serve a useful purpose if acceleration could be sustained throughout it?

Only in a highly speculative role: it is a railgun concept suited to interplanetary ranges rather than a conventional naval gun.

The viewer asks whether any useful gun could have a barrel roughly 400 calibres long if its propulsive system sustained the projectile throughout that distance. The premise is closer to a railgun than a conventional chemically powered cannon. Maintaining acceleration over such a length would suit ranges measured between planetary bodies rather than ordinary naval combat. The response is a speculative future-weapons thought experiment, and it does not identify a historical weapon built to those proportions.