Just a few notes,
1) The "F" in front of the number just stands for "Fighter"... No big deal really...
2) During the Cold War, the USA even gave "F" codes to Soviet aircraft, e.g. the MiG-21 Fishbed was designated the YF-110. The "Y" is added for any experimental fighter aircraft. In this case, it's cause "acquired" MiGs were used for experiments & testing. YF-113 was the designation given to the MiG-23. However, the use of the "F" series for Soviet aircraft was later abandoned.
3) Besides the Soviets, the Americans also labeled the Isreali IAI Kfir jet, the F-21. This designation remains even though the US dropped using the "F" series on all other foreign fighters.
4) The Hornet is labeled F/A-18, standing for Fighter and Attack.
5) The "F" system has sometimes not been applied properly, for example, the JSF will be labeled the F-35 instead of the next number in the series which is F-24. The reason for skipping so many numbers is because the JSF used to be called the X-35 (under eXperimental series)... and when the needed to switch it over to the "F" series, they felt it was more convenient just to change the letter in front...
For some more info on the Unified Numbering Series, go to:
http://www.aerospaceweb.org/question/history/q0012.shtml