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The largest integer such that all smaller integers relatively prime to it are either a prime, a power of a prime, or 1. [Noe] The smallest number which is the sum of two odd primes in six different ways. [Wolman] The smallest composite number which is the order of a simple group, namely A5 (the alternating group on 5 letters). [Terr] The largest known positive integer that cannot be written as p * q + r, where p, q, r are three distinct primes. [Capelle]
(There are 4 curios for this number that have not yet been approved by an editor.)
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