vim, 70 bytes

Result

WA

Code [DL]

00000000  6c 71 79 22 61 64 30 73  12 3d 40 61 2a 32 2b 40  |lqy"ad0s.=@a*2+@|
00000010  40 0a 1b 6c 71 49 30 1b  5e 6c 36 40 79 22 62 63  |@..lqI0.^l6@y"bc|
00000020  63 12 3d 66 6d 6f 64 28  73 71 72 74 28 40 63 2a  |c.=fmod(sqrt(@c*|
00000030  38 2b 31 29 2c 31 29 3d  3d 30 0a 1b 6a 5e 71 34  |8+1),1)==0..j^q4|
00000040  39 40 7a 5a 5a 0a                                 |9@zZZ.|
00000046

Disassembly

lqy"ad0s<C-R>=@a*2+@@<NL><Esc>lqI0<Esc>^l6@y"bcc<C-R>=fmod(sqrt(@c*8+1),1)==0<NL><Esc>j^q49@zZZ<NL>

stdin

11101010
00000100
00100101
10100111
11101111
10110011
10110101
00011100
10111110
00000110
01111001
01111000
00010101
11101000
00001010
00000000
01001110
01011110
10110111
10110000
01000010
00001111
11111101
11100110
01100011
10011001
00100100
01100000
00111101
10110001
11001010
11001101
00011100
11001001
01011011
10101011
11010001
11000101
01110111
00000011
00111000
11100111
00000001
00101101
10000000
10001000
01101001
00110111
01101001
11010010

stdout

1
00000100
00100101
10100111
11101111
10110011
10110101
00011100
10111110
00000110
01111001
01111000
00010101
11101000
00001010
00000000
01001110
01011110
10110111
10110000
01000010
00001111
11111101
11100110
01100011
10011001
00100100
01100000
00111101
10110001
11001010
11001101
00011100
11001001
01011011
10101011
11010001
11000101
01110111
00000011
00111000
11100111
00000001
00101101
10000000
10001000
01101001
00110111
01101001
11010010

stderr

strace