7

This number is a prime.

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The sum of all untouchable primes. [Loungrides]

The smallest of only two primes less than a titanic prime of the form p^p+p+1, where p is a prime. The other is 31. [Loungrides]

(7, 11, 13) is the first consecutive prime number triple (p, q, r) such that r divides pq+1. Note that the quotient is 6 (the first perfect number). [Loungrides]

The only non-titanic prime of form n^n+3, i.e., 2^2+3. [Loungrides]

If p is a prime greater or equal to 7 then any repunit number consisting of p-1 one’s is divisible by p. [Loungrides]