5077
This number is a prime.
The first term of six prime numbers in arithmetic progression with a common difference of 9876543210. [Honaker]
The smallest conductor of a rank 3 elliptic curve. Note that 5077a1 is called the “Gauss curve”. [Lozano-Robledo]
5077 is an unhappy prime, but 5077*2^2198565-1 is a happy prime containing 661838 digits. Found by J. K. Andersen, 2008. [Rivera]
The last of the original 13 colonies (Rhode Island) to
ratify the constitution did so 5077 days after the
declaration of independence (May 29, 1790). [Gaydos]
The largest prime whose square has its every digit
occurring exactly twice: 50772 = 25775929.
Coincidentally, the smallest such prime is obtained by
deleting a digit from 5077, i.e., 577. [Gudipati]