19

This number is a prime.

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There are 19 Sophie Germain primes whose sums of reciprocals of digits equal one. The smallest is 86843 and the largest is 98689889. [Gaydos]

The binary representation of 10^19 contains 19 ones. [Gaydos]

There are 19 brilliant numbers with digits in strictly descending order. [Gaydos]

The sum of the four 3-letter integers (one+two+six+ten). [Gaydos]

19^19 is in a prime gap of length 19. [Gaydos]