Philip Bump points out that despite the number of people running for president, it’s not the record.
“Taken literally, nearly 2,500 people have run for president since 1980, in the sense that they filled out the requisite form with the Federal Election Commission (which is remarkably trivial to do). Since many have run multiple times, it’s a grand total of more than 3,100 separate candidacies. For elections that have produced a total of five different presidents.”
What constitutes a “real” candidate? Bump uses a “subjective objective definition: Appearances on Wikipedia. Let the wisdom of the crowd tell us who is considered real or not!”