Since the unification of the numbering system in 1962, US fighters have been designated by consecutive numbers, beginning with the F-1 Fury. F-13 was never assigned (presumably due to triskaidekaphobia among pilots, who are notoriously superstitious), but after the F/A-18 Hornet, the next announced aircraft was the F-20 Tigershark.
There have been several theories put forth to explain the omission.
The most prevalent theory in the 1980s was that it was the designation of the stealth fighter whose development was an open secret in the aerospace community. In 1986, the Testor Corporation released a model aircraft kit, calling it the "F-19 Stealth Fighter", and in the same year, the Tom Clancy novel Red Storm Rising mentioned an "F-19 Ghostrider".
When the actual aircraft was publicly revealed in 1988, it was called the F-117 Nighthawk (an odd designation, although Joe Baugher asserts that the first manuals had the meaningless number "F-117" on the cover, and the designation stuck, despite the apparent connection to the old series of fighter numbers). There seems not to be any evidence that "F-19" was ever used to designate the Nighthawk, although the USAF Museum website (as of 2003) does include the cryptic entry "Lockheed F-19 CSIRS (see F-117)".
At one point, a USAF spokesman claimed that it was to avoid confusion with the MiG-19, but this seems never to have interfered with the use of 17, 21, and 23 for instance.
Another theory is that Northrop requested "F-20" for their new design, (similar to the World War II-era skip over "P-74" to allow General Motors to use "P-75" for a new fighter), but this is most likely an urban legend.
It is possible that the "F-19" exists, but is still classified - a number of projects have been kept secret for many years - or simply that the designation was left open to confuse foreign intelligence agencies.
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