At one time, the entry for this Nathaniel Barnum showed a death date of 5 February 1778 and a will date of 5 February 1778/79, based upon undocumented research by a Barnum descendant. However, an inventory was subsequently found for the estate of Nathaniel Barnum, dated 1 Nov 1757 and approved 6 Mar 1758. The executrix of the estate was Mrs. Thankful Barnum. It appears that the inventory applies to the subject of this entry, Nathaniel Barnum born 1701, son of Richard Barnum and Mary Hurd.
The earlier death and will dates, then, must either be errors or must apply to a different Nathaniel Barnum. Although it's tempting to assign that death date to Nathaniel Barnum born in 1745, a son of this Nathaniel, the Genealogical Record of the Barnum Family shows that son as living and fathering children as late as 1785.