13

This number is a prime.

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Photo credit: Patrick Kik

prime(13) = reversal(sigma(13)). It is the only multidigit number with this property. [Firoozbakht]

The floor function of e^e - phi^phi, where phi is Golden Ratio. [Firoozbakht]

5*11 - 2*3*7 = 13 (first six primes). [Firoozbakht]

13^13 - π(13)^π(13) is prime. It is the largest known prime with this property. The next prime of this form (if it exists) will have more than 50000 digits. [Firoozbakht]

π(π(1) + π(2) + ... + π(13)) = sigma(13). It is the only number with this property. [Firoozbakht]