With less than 2 miles of tarmac to its name, the A751 doesn't seem much of a road at first glance, running from the three-house hamlet of Innermessan on the A77 through a smattering of farmhouses, the last of which, Inchparks, has the good fortune to lie on a corner with the A75. The nearest settlement to Inchparks is Aird, which arguably pales in comparison to Innermessan.
The point of this road is to get traffic from the A75 - that is, heading to or from Dumfries, Gretna and basically the whole of England - to Cairnryan, the ferry port for the fast catamarans to Larne, Northern Ireland, without having to negotiate central Stranraer. Given that Stranraer town centre is a port all of its own (although the passenger ferries currently all go from Cairnryan), this makes good sense. Ayrshire traffic can equally use the A751 to get to the Whithorn peninsula, which is beautiful if sparse countryside.
The A751 has remained steadfastly unchanged since the number was slapped upon it some time in the late 1920s. It is one of those Scottish quasi-primary roads like the A73 or A703, with a mixture of green and white signs at each end, while maps also disagree on what colour the line should be. Given that the road is maintained for Transport Scotland by Amey, that's a pretty compelling vote for primary status.