When the 2012 puzzle ended, 3301 released a final message entitled Valēte!. The message ended with a post-scriptum (PS) containing a large number. It became known in the community as the "PS number" and stands unused.
P.S. 1041279065891998535982789873959431895640\ 442510695567564373922695237268242385295908173\ 9834390370374475764863415203423499357108713631
Trailing backslashes are commonly used in programming languages to break up long lines. The full number is:
10412790658919985359827898739594318956404425106955675643739226952372682423852959081739834390370374475764863415203423499357108713631
A RSA modulus?
Interestingly, it's not a prime number as it factors into two large prime numbers:
p = 99554414790940424414351515490472769096534141749790794321708050837 q = 104593961812606247801193807142122161186583731774511103180935025763
Thus, it could be interpreted as a RSA public key (assuming the exponent to be 65537, an almost universal value). As RSA had been used by 3301 during the 2012 puzzle, this theory is particularly appealing.
Furthermore, the PS number has a bit length of 432 bits. In 2014, an second RSA puzzle involved a number with a modulus of the same size: according to some, the PS number could have been a experiment whether solvers would have been able to break a RSA key of this size, which wasn't trivial.
Finally, the two prime factors both have a bit length of 216 (= 432 / 2). This matches the behavior of the Perl library 3301 used in 2012 and 2014, Crypt::RSA: given an even output modulus size n, the two prime factors are generated to be of bit length n / 2.