List of prime numbers in binary from 0 to 2¹⁶. Because I was searching for this and couldn’t find it.

0000000000000010
0000000000000011
0000000000000101
0000000000000111
0000000000001011
0000000000001101
0000000000010001
0000000000010011
0000000000010111
0000000000011101
0000000000011111
0000000000100101
0000000000101001
0000000000101011
0000000000101111
0000000000110101
0000000000111011
0000000000111101
0000000001000011
0000000001000111
0000000001001001
0000000001001111
0000000001010011
0000000001011001
0000000001100001
0000000001100101
0000000001100111
0000000001101011
0000000001101101
0000000001110001
0000000001111111
0000000010000011
0000000010001001
0000000010001011
0000000010010101
0000000010010111
0000000010011101
0000000010100011
0000000010100111
0000000010101101
0000000010110011
0000000010110101
0000000010111111
0000000011000001
0000000011000101
0000000011000111
0000000011010011
0000000011011111
0000000011100011
0000000011100101
0000000011101001
0000000011101111
0000000011110001
0000000011111011
0000000100000001
0000000100000111
0000000100001101
0000000100001111
0000000100010101
0000000100011001
0000000100011011
0000000100100101
0000000100110011
0000000100110111
0000000100111001
0000000100111101
0000000101001011
0000000101010001
0000000101011011
0000000101011101
0000000101100001
0000000101100111
0000000101101111
0000000101110101
0000000101111011
0000000101111111
0000000110000101
0000000110001101
0000000110010001
0000000110011001
0000000110100011
0000000110100101
0000000110101111
0000000110110001
0000000110110111
0000000110111011
0000000111000001
0000000111001001
0000000111001101
0000000111001111
0000000111010011
0000000111011111
0000000111100111
0000000111101011
0000000111110011
0000000111110111
0000000111111101
0000001000001001
0000001000001011
0000001000011101
0000001000100011
0000001000101101
0000001000110011
0000001000111001
0000001000111011
0000001001000001
0000001001001011
0000001001010001
0000001001010111
0000001001011001
0000001001011111
0000001001100101
0000001001101001
0000001001101011
0000001001110111
0000001010000001
0000001010000011
0000001010000111
0000001010001101
0000001010010011
0000001010010101
0000001010100001
0000001010100101
0000001010101011
0000001010110011
0000001010111101
0000001011000101
0000001011001111
0000001011010111
0000001011011101
0000001011100011
0000001011100111
0000001011101111
0000001011110101
0000001011111001
0000001100000001
0000001100000101
0000001100010011
0000001100011101
0000001100101001
0000001100101011
0000001100110101
0000001100110111
0000001100111011
0000001100111101
0000001101000111
0000001101010101
0000001101011001
0000001101011011
0000001101011111
0000001101101101
0000001101110001
0000001101110011
0000001101110111
0000001110001011
0000001110001111
0000001110010111
0000001110100001
0000001110101001
0000001110101101
0000001110110011
0000001110111001
0000001111000111
0000001111001011
0000001111010001
0000001111010111
0000001111011111
0000001111100101
0000001111110001
0000001111110101
0000001111111011
0000001111111101
0000010000000111
0000010000001001
0000010000001111
0000010000011001
0000010000011011
0000010000100101
0000010000100111
0000010000101101
0000010000111111
0000010001000011
0000010001000101
0000010001001001
0000010001001111
0000010001010101
0000010001011101
0000010001100011
0000010001101001
0000010001111111
0000010010000001
0000010010001011
0000010010010011
0000010010011101
0000010010100011
0000010010101001
0000010010110001
0000010010111101
0000010011000001
0000010011000111
0000010011001101
0000010011001111
0000010011010101
0000010011100001
0000010011101011
0000010011111101
0000010011111111
0000010100000011
0000010100001001
0000010100001011
0000010100010001
0000010100010101
0000010100010111
0000010100011011
0000010100100111
0000010100101001
0000010100101111
0000010101010001
0000010101010111
0000010101011101
0000010101100101
0000010101110111
0000010110000001
0000010110001111
0000010110010011
0000010110010101
0000010110011001
0000010110011111
0000010110100111
0000010110101011
0000010110101101
0000010110110011
0000010110111111
0000010111001001
0000010111001011
0000010111001111
0000010111010001
0000010111010101
0000010111011011
0000010111100111
0000010111110011
0000010111111011
0000011000000111
0000011000001101
0000011000010001
0000011000010111
0000011000011111
0000011000100011
0000011000101011
0000011000101111
0000011000111101
0000011001000001
0000011001000111
0000011001001001
0000011001001101
0000011001010011
0000011001010101
0000011001011011
0000011001100101
0000011001111001
0000011001111111
0000011010000011
0000011010000101
0000011010011101
0000011010100001
0000011010100011
0000011010101101
0000011010111001
0000011010111011
0000011011000101
0000011011001101
0000011011010011
0000011011011001
0000011011011111
0000011011110001
0000011011110111
0000011011111011
0000011011111101
0000011100001001
0000011100010011
0000011100011111
0000011100100111
0000011100110111
0000011101000101
0000011101001011
0000011101001111
0000011101010001
0000011101010101
0000011101010111
0000011101100001
0000011101101101
0000011101110011
0000011101111001
0000011110001011
0000011110001101
0000011110011101
0000011110011111
0000011110110101
0000011110111011
0000011111000011
0000011111001001
0000011111001101
0000011111001111
0000011111010011
0000011111011011
0000011111100001
0000011111101011
0000011111101101
0000011111110111
0000100000000101
0000100000001111
0000100000010101
0000100000100001
0000100000100011
0000100000100111
0000100000101001
0000100000110011
0000100000111111
0000100001000001
0000100001010001
0000100001010011
0000100001011001
0000100001011101
0000100001011111
0000100001101001
0000100001110001
0000100010000011
0000100010011011
0000100010011111
0000100010100101
0000100010101101
0000100010111101
0000100010111111
0000100011000011
0000100011001011
0000100011011011
0000100011011101
0000100011100001
0000100011101001
0000100011101111
0000100011110101
0000100011111001
0000100100000101
0000100100000111
0000100100011101
0000100100100011
0000100100100101
0000100100101011
0000100100101111
0000100100110101
0000100101000011
0000100101001001
0000100101001101
0000100101001111
0000100101010101
0000100101011001
0000100101011111
0000100101101011
0000100101110001
0000100101110111
0000100110000101
0000100110001001
0000100110001111
0000100110011011
0000100110100011
0000100110101001
0000100110101101
0000100111000111
0000100111011001
0000100111100011
0000100111101011
0000100111101111
0000100111110101
0000100111110111
0000100111111101
0000101000010011
0000101000011111
0000101000100001
0000101000110001
0000101000111001
0000101000111101
0000101001001001
0000101001010111
0000101001100001
0000101001100011
0000101001100111
0000101001101111
0000101001110101
0000101001111011
0000101001111111
0000101010000001
0000101010000101
0000101010001011
0000101010010011
0000101010010111
0000101010011001
0000101010011111
0000101010101001
0000101010101011
0000101010110101
0000101010111101
0000101011000001
0000101011001111
0000101011011001
0000101011100101
0000101011100111
0000101011101101
0000101011110001
0000101011110011
0000101100000011
0000101100010001
0000101100010101
0000101100011011
0000101100100011
0000101100101001
0000101100101101
0000101100111111
0000101101000111
0000101101010001
0000101101010111
0000101101011101
0000101101100101
0000101101101111
0000101101111011
0000101110001001
0000101110001101
0000101110010011
0000101110011001
0000101110011011
0000101110110111
0000101110111001
0000101111000011
0000101111001011
0000101111001111
0000101111011101
0000101111100001
0000101111101001
0000101111110101
0000101111111011
0000110000000111
0000110000001011
0000110000010001
0000110000100101
0000110000101111
0000110000110001
0000110001000001
0000110001011011
0000110001011111
0000110001100001
0000110001101101
0000110001110011
0000110001110111
0000110010000011
0000110010001001
0000110010010001
0000110010010101
0000110010011101
0000110010110011
0000110010110101
0000110010111001
0000110010111011
0000110011000111
0000110011100011
0000110011100101
0000110011101011
0000110011110001
0000110011110111
0000110011111011
0000110100000001
0000110100000011
0000110100001111
0000110100010011
0000110100011111
0000110100100001
0000110100101011
0000110100101101
0000110100111101
0000110100111111
0000110101001111
0000110101010101
0000110101101001
0000110101111001
0000110110000001
0000110110000101
0000110110000111
0000110110001011
0000110110001101
0000110110100011
0000110110101011
0000110110110111
0000110110111101
0000110111000111
0000110111001001
0000110111001101
0000110111010011
0000110111010101
0000110111011011
0000110111100101
0000110111100111
0000110111110011
0000110111111101
0000110111111111
0000111000001001
0000111000010111
0000111000011101
0000111000100001
0000111000100111
0000111000101111
0000111000110101
0000111000111011
0000111001001011
0000111001010111
0000111001011001
0000111001011101
0000111001101011
0000111001110001
0000111001110101
0000111001111101
0000111010000111
0000111010001111
0000111010010101
0000111010011011
0000111010110001
0000111010110111
0000111010111001
0000111011000011
0000111011010001
0000111011010101
0000111011011011
0000111011101101
0000111011101111
0000111011111001
0000111100000111
0000111100001011
0000111100001101
0000111100010111
0000111100100101
0000111100101001
0000111100110001
0000111101000011
0000111101000111
0000111101001101
0000111101001111
0000111101010011
0000111101011001
0000111101011011
0000111101100111
0000111101101011
0000111101111111
0000111110010101
0000111110100001
0000111110100011
0000111110100111
0000111110101101
0000111110110011
0000111110110101
0000111110111011
0000111111010001
0000111111010011
0000111111011001
0000111111101001
0000111111101111
0000111111111011
0000111111111101
0001000000000011
0001000000001111
0001000000011111
0001000000100001
0001000000100101
0001000000101011
0001000000111001
0001000000111101
0001000000111111
0001000001010001
0001000001101001
0001000001110011
0001000001111001
0001000001111011
0001000010000101
0001000010000111
0001000010010001
0001000010010011
0001000010011101
0001000010100011
0001000010100101
0001000010101111
0001000010110001
0001000010111011
0001000011000001
0001000011001001
0001000011100111
0001000011110001
0001000011110011
0001000011111101
0001000100000101
0001000100001011
0001000100010101
0001000100100111
0001000100101101
0001000100111001
0001000101000101
0001000101000111
0001000101011001
0001000101011111
0001000101100011
0001000101101001
0001000101101111
0001000110000001
0001000110000011
0001000110001101
0001000110011011
0001000110100001
0001000110100101
0001000110100111
0001000110101011
0001000111000011
0001000111000101
0001000111010001
0001000111010111
0001000111100111
0001000111101111
0001000111110101
0001000111111011
0001001000001101
0001001000011101
0001001000011111
0001001000100011
0001001000101001
0001001000101011
0001001000110001
0001001000110111
0001001001000001
0001001001000111
0001001001010011
0001001001011111
0001001001110001
0001001001110011
0001001001111001
0001001001111101
0001001010001111
0001001010010111
0001001010101111
0001001010110011
0001001010110101
0001001010111001
0001001010111111
0001001011000001
0001001011001101
0001001011010001
0001001011011111
0001001011111101
0001001100000111
0001001100001101
0001001100011001
0001001100100111
0001001100101101
0001001100110111
0001001101000011
0001001101000101
0001001101001001
0001001101001111
0001001101010111
0001001101011101
0001001101100111
0001001101101001
0001001101101101
0001001101111011
0001001110000001
0001001110000111
0001001110001011
0001001110010001
0001001110010011
0001001110011101
0001001110011111
0001001110101111
0001001110111011
0001001111000011
0001001111010101
0001001111011001
0001001111011111
0001001111101011
0001001111101101
0001001111110011
0001001111111001
0001001111111111
0001010000011011
0001010000100001
0001010000101111
0001010000110011
0001010000111011
0001010001000101
0001010001001101
0001010001011001
0001010001101011
0001010001101111
0001010001110001
0001010001110101
0001010010001101
0001010010011001
0001010010011111
0001010010100001
0001010010110001
0001010010110111
0001010010111101
0001010011001011
0001010011010101
0001010011100011
0001010011100111
0001010100000101
0001010100001011
0001010100010001
0001010100010111
0001010100011111
0001010100100101
0001010100101001
0001010100101011
0001010100110111
0001010100111101
0001010101000001
0001010101000011
0001010101001001
0001010101011111
0001010101100101
0001010101100111
0001010101101011
0001010101111101
0001010101111111
0001010110000011
0001010110001111
0001010110010001
0001010110010111
0001010110011011
0001010110110101
0001010110111011
0001010111000001
0001010111000101
0001010111001101
0001010111010111
0001010111110111
0001011000000111
0001011000001001
0001011000001111
0001011000010011
0001011000010101
0001011000011001
0001011000011011
0001011000100101
0001011000110011
0001011000111001
0001011000111101
0001011001000101
0001011001001111
0001011001010101
0001011001101001
0001011001101101
0001011001101111
0001011001110101
0001011010010011
0001011010010111
0001011010011111
0001011010101001
0001011010101111
0001011010110101
0001011010111101
0001011011000011
0001011011001111
0001011011010011
0001011011011001
0001011011011011
0001011011100001
0001011011100101
0001011011101011
0001011011101101
0001011011110111
0001011011111001
0001011100001001
0001011100001111
0001011100100011
0001011100100111
0001011100110011
0001011101000001
0001011101011101
0001011101100011
0001011101110111
0001011101111011
0001011110001101
0001011110010101
0001011110011011
0001011110011111
0001011110100101
0001011110110011
0001011110111001
0001011110111111
0001011111001001
0001011111001011
0001011111010101
0001011111100001
0001011111101001
0001011111110011
0001011111110101
0001011111111111
0001100000000111
0001100000010011
0001100000011101
0001100000110101
0001100000110111
0001100000111011
0001100001000011
0001100001001001
0001100001001101
0001100001010101
0001100001100111
0001100001110001
0001100001110111
0001100001111101
0001100001111111
0001100010000101
0001100010001111
0001100010011011
0001100010011101
0001100010100111
0001100010101101
0001100010110011
0001100010111001
0001100011000001
0001100011000111
0001100011010001
0001100011010111
0001100011011001
0001100011011111
0001100011100101
0001100011101011
0001100011110101
0001100011111101
0001100100010101
0001100100011011
0001100100110001
0001100100110011
0001100101000101
0001100101001001
0001100101010001
0001100101011011
0001100101111001
0001100110000001
0001100110010011
0001100110010111
0001100110011001
0001100110100011
0001100110101001
0001100110101011
0001100110110001
0001100110110101
0001100111000111
0001100111001111
0001100111011011
0001100111101101
0001100111111101
0001101000000011
0001101000000101
0001101000010001
0001101000010111
0001101000100001
0001101000100011
0001101000101101
0001101000101111
0001101000110101
0001101000111111
0001101001001101
0001101001010001
0001101001101001
0001101001101011
0001101001111011
0001101001111101
0001101010000111
0001101010001001
0001101010010011
0001101010100111
0001101010101011
0001101010101101
0001101010110001
0001101010111001
0001101011001001
0001101011001111
0001101011010101
0001101011010111
0001101011100011
0001101011110011
0001101011111011
0001101011111111
0001101100000101
0001101100100011
0001101100100101
0001101100101111
0001101100110001
0001101100110111
0001101100111011
0001101101000001
0001101101000111
0001101101001111
0001101101010101
0001101101011001
0001101101100101
0001101101101011
0001101101110011
0001101101111111
0001101110000011
0001101110010001
0001101110011101
0001101110100111
0001101110111111
0001101111000101
0001101111010001
0001101111010111
0001101111011001
0001101111101111
0001101111110111
0001110000001001
0001110000010011
0001110000011001
0001110000100111
0001110000101011
0001110000101101
0001110000110011
0001110000111101
0001110001000101
0001110001001011
0001110001001111
0001110001010101
0001110001110011
0001110010000001
0001110010001011
0001110010001101
0001110010011001
0001110010100011
0001110010100101
0001110010110101
0001110010110111
0001110011001001
0001110011100001
0001110011110011
0001110011111001
0001110100001001
0001110100011011
0001110100100001
0001110100100011
0001110100110101
0001110100111001
0001110100111111
0001110101000001
0001110101001011
0001110101010011
0001110101011101
0001110101100011
0001110101101001
0001110101110001
0001110101110101
0001110101111011
0001110101111101
0001110110000111
0001110110001001
0001110110010101
0001110110011001
0001110110011111
0001110110100101
0001110110100111
0001110110110011
0001110110110111
0001110111000101
0001110111010111
0001110111011011
0001110111100001
0001110111110101
0001110111111001
0001111000000001
0001111000000111
0001111000001011
0001111000010011
0001111000010111
0001111000100101
0001111000101011
0001111000101111
0001111000111101
0001111001001001
0001111001001101
0001111001001111
0001111001101101
0001111001110001
0001111010001001
0001111010001111
0001111010010101
0001111010100001
0001111010101101
0001111010111011
0001111011000001
0001111011000101
0001111011000111
0001111011001011
0001111011011101
0001111011100011
0001111011101111
0001111011110111
0001111011111101
0001111100000001
0001111100001101
0001111100001111
0001111100011011
0001111100111001
0001111101001001
0001111101001011
0001111101010001
0001111101100111
0001111101110101
0001111101111011
0001111110000101
0001111110010001
0001111110010111
0001111110011001
0001111110011101
0001111110100101
0001111110101111
0001111110110101
0001111110111011
0001111111010011
0001111111100001
0001111111100111
0001111111101011
0001111111110011
0001111111111111
0010000000010001
0010000000011011
0010000000011101
0010000000100111
0010000000101001
0010000000101101
0010000000110011
0010000001000111
0010000001001101
0010000001010001
0010000001011111
0010000001100011
0010000001100101
0010000001101001
0010000001110111
0010000001111101
0010000010001001
0010000010100001
0010000010101011
0010000010110001
0010000010111001
0010000011000011
0010000011000101
0010000011100011
0010000011100111
0010000011101101
0010000011101111
0010000011111011
0010000011111111
0010000100001101
0010000100010011
0010000100110101
0010000101000001
0010000101001001
0010000101001111
0010000101011001
0010000101011011
0010000101011111
0010000101110011
0010000101111101
0010000110000101
0010000110010101
0010000110010111
0010000110100001
0010000110101111
0010000110110011
0010000110110101
0010000111000001
0010000111000111
0010000111010111
0010000111011101
0010000111100101
0010000111101001
0010000111110001
0010000111110101
0010000111111011
0010001000000011
0010001000001001
0010001000001111
0010001000011011
0010001000100001
0010001000100101
0010001000101011
0010001000110001
0010001000111001
0010001001001011
0010001001001111
0010001001100011
0010001001100111
0010001001110011
0010001001110101
0010001001111111
0010001010000101
0010001010000111
0010001010010001
0010001010011101
0010001010011111
0010001010100011
0010001010110111
0010001010111101
0010001011011011
0010001011100001
0010001011100101
0010001011101101
0010001011110111
0010001100000011
0010001100001001
0010001100001011
0010001100100111
0010001100101001
0010001100101111
0010001100110011
0010001100110101
0010001101000101
0010001101010001
0010001101010011
0010001101011001
0010001101100011
0010001101101011
0010001110000011
0010001110001111
0010001110010101
0010001110100111
0010001110101101
0010001110110001
0010001110111111
0010001111000101
0010001111001001
0010001111010101
0010001111011101
0010001111100011
0010001111101111
0010001111110011
0010001111111001
0010010000000101
0010010000001011
0010010000010111
0010010000011001
0010010000101001
0010010000111101
0010010001000001
0010010001000011
0010010001001101
0010010001011111
0010010001100111
0010010001101011
0010010001111001
0010010001111101
0010010001111111
0010010010000101
0010010010011011
0010010010100001
0010010010101111
0010010010110101
0010010010111011
0010010011000101
0010010011001011
0010010011001101
0010010011010111
0010010011011001
0010010011011101
0010010011011111
0010010011110101
0010010011110111
0010010011111011
0010010100000001
0010010100000111
0010010100010011
0010010100011001
0010010100100111
0010010100110001
0010010100111101
0010010101000011
0010010101001011
0010010101001111
0010010101110011
0010010110000001
0010010110001101
0010010110010011
0010010110010111
0010010110011101
0010010110011111
0010010110101011
0010010110110001
0010010110111101
0010010111001101
0010010111001111
0010010111011001
0010010111100001
0010010111110111
0010010111111001
0010011000000101
0010011000001011
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1111111111110001

Python script to reproduce

def primes_upto(limit):
    prime = [True] * limit
    for n in range(2, limit):
        if prime[n]:
            yield f'{n:016b}' # n is a prime
            for c in range(n*n, limit, n):
                prime[c] = False # mark composites

list(primes_upto(int(16 * '1', 2)))