Sort of a tough question-buying a gun just because of the serial number.
Suppose it was a bolt-action Mossberg 12 ga. shotgun that had, for a serial number, the one number that really caught your attention like your birth date, your anniversary date (with the current spouse

) or 666 or, whatever.
Would you buy it? I suppose there are those who collect Mossberg or similar bolt-actions, but probably not many.
But I wouldn't buy it at most any price.
So, really, the gun first has to catch my attention enough to pick it up an examine it. Then, if I noted the serial number and that number "spoke" to me, maybe I'd buy it.
But, again, it would depend on brand/model, condition and, perhaps, caliber.
But, no bolt-action Mossbergs (heck, most oldies weren't serial numbered anyway).
Bob