[ May 25, 1999 ]
A square that is a palindrome in binary

4770504939 ² = 22757717373023393721

yielding the following beautiful palindrome when converted into binary

10011101111010011101001110110000000001101110010111001011110111001

Entry in Sloane's Online Encyclopedia is sequence A003166.

The complete list of all known squares that are palindromic in binary
Palindromic numbers beyond base 10
It grew over the years and the length of the largest binary square is now 157 digits !