19

This number is a prime.

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phi(19) - π(19) = 1 + 9. 19 is the only prime with this property. [Firoozbakht]

Both numbers reversal(19! - 1) and reversal(19! + 1) are primes. 19 is the largest known prime with this property. [Firoozbakht]

19 is the only known prime of the form n^n - 8. The next prime in this form (if it exists) will have more than 34000 digits. [Firoozbakht]

Only known prime of the form p*prime(p)^p + 1, where p is prime. [Firoozbakht]

19 = sigma(1*9) + phi(1*9). It is the only known prime with this property. [Firoozbakht]