The 20th century musical Damn Yankees had a successful run of 1019 performances. [Williams]
The smallest number with a period length more than 1000 digits. [Pimentel]
(e^((e^)) = (e^(23.14...)) = (e^9) = (8103.08...) = 1019 is prime. [Kulsha]
The sum of the squares of the first three Mersenne primes. [Silva]
The smallest prime such that its cube (1058089859) is equal to the sum of a prime and its reversal, i.e., 297594067 + 760495792. [Rivera]
The smallest invertible prime of the form 4n^2+4n+59.
The lesser term in the first twin prime pair (p, q) such that p#+1 and q#+1 are both primes. [Loungrides]
(There are 5 curios for this number that have not yet been approved by an editor.)