11

This number is a prime.

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10! - 11 and 10! + 11 are two consecutive primes. [Firoozbakht]

11 = π(11) + π(π(11)) + .... It is the largest such number. [Firoozbakht]

The only known multidigit prime of the form prime(n)^n + n. The next such prime if it exists has more than 30000 digits. [Firoozbakht]

The first 1+1 digits of π(11^11) are 11. [Firoozbakht]

2! + 3! + 5! = 7 (mod 11). There exists only one other known prime with this property. [Firoozbakht]

2*3*5*...*prime(11) = 11 (mod 11+1). It is the only known prime with this property. [Firoozbakht]

π(π(1) + π(2) + ... + π(11)) = 11. It is the only number with this property. [Firoozbakht]