You are correct, 21 US presidents have been reelected directly following their first term, a 22nd president Grover Cleveland was elected to a second non-consecutive term in the 1892 election after losing reelection to Grover Cleveland in 1888.

Some other interesting facts about US politics:
There have been 5 presidential election where the winner did not win the popular vote, the first in 1824
Some US states hold Caucuses instead of primary elections
George Washington did not run for a third term, fearing that if he died in office many would view the presidency as a lifetime appointment; he in fact died in the time period that would have been his third term
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