George F Pinkham is shown in the Vital Records of Nantucket (1850) as having been born in 1824. His parents were George C Pinkham, b. 27 Aug 1791, Nantucket, and Phebe Swain (who apparently was illegitimate). The line goes back: George Pinkham m. Deborah Coffin, William Pinkham m. Phebe Wyer, Barnabas Pinkham m. Priscilla Gardner, Richard Pinkham m. Mary Coffin, and finally the original Richard Pinkham m. Gylian (?). If you need any further help with this line just e-mail me.
I would appreciate learning the spouse of George F Pinkham and any descendants you may have.