# Carmichael Number has 3 Odd Prime Factors

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## Theorem

Let $n$ be a Carmichael number.

Then $n$ has at least $3$ distinct prime factors.

## Historical Note

Robert Daniel Carmichael proved that a Carmichael Number has at least 3 distinct odd prime factors in $1912$, at around the same time that he discovered that $561$ was the smallest one.