It's the palindromic primes which only use digits 1 and 0! There are 49 of them below 10^20-1 and probably an infinite number above 10^20-1. Here's the first 49...

Palindomic Primes Composed of Only 1's and 0's < 10^20-1
11 101 100111001 110111011 111010111 1100011100011 1100101010011
1101010101011 1110110110111 1110111110111 100110101011001 101000010000101 101011000110101 101110000011101
110011101110011 111100111001111 10000010101000001 10011010001011001 10100110001100101 10110010001001101 10110101110101101
10111000000011101 10111101110111101 10111110101111101 11010001010001011 11100110001100111 1000010101010100001 1001010100010101001
1001011111111101001 1001100110110011001 1010000101010000101 1010001001001000101 1010001110111000101 1010011000001100101 1010111011101110101
1011001000001001101 1011010011100101101 1011100010100011101 1011101011101011101 1011111110111111101 1100010100010100011 1100010110110100011
1100011011101100011 1101001100011001011 1101101110111011011 1110001101011000111 1111001001001001111 1111001101011001111 1111111111111111111

If you are wondering what palindromic means, with respect to numbers it refers to a number which reads the same forwards as backwards (like 12321).  A palindromic prime is a prime number which reads the same forwards as backwards (like 313).

Edit: I submitted this sequence to the OEIS on Nov 29.  Today, it was accepted. Yay!