The first utility patent issued under the 1836 U.S. patent system was assigned number 1.
Patent No. 1 was issued on July 13, 1836, to John Ruggles for an improvement to traction wheels used on steam locomotives. The number began the sequential series still used for ordinary U.S. utility patents. Ruggles was also a senator from Maine and a key supporter of the legislation that reorganized the patent system.
This numbering system followed the Patent Act of 1836, which created a more rigorous examination process and reorganized the Patent Office. Earlier U.S. patents, issued from 1790 through July 1836, were not originally numbered. After the Patent Office fire of December 1836 destroyed many records, surviving or reconstructed earlier patents were given retroactive numbers with an “X” prefix.
That history creates a frequent confusion: the first U.S. patent ever granted was issued to Samuel Hopkins in 1790, but it was not originally called Patent No. 1. The question’s reference to the 1836 system specifically points to the new sequential series, whose first number was 1.