Room 3 of the Maze

Question

Exhausted from the effort of solving Room 2, you try to get a good night's sleep, but your sleep is interrupted by vivid dreams of fblthps, numbers, and vectors. The Maze is getting to you a bit, it seems. Once you feel awake and ready, you read the note suspended, as usual, in the middle of the room.

The Third Room! Only one other person has made it this far and well...it's quite unfortunate that he had no nails left when we finally got him through the portal.
This room is easier than room 2, but the information is more hidden. In the interest of keeping our test subjects from dropping like flies, we have decided to include an example value of Key 2 and its corresponding answer. This way, if you think you have cracked the puzzle, you can replicate your steps on the example Key and see if your answer matches its. Take a look at the information below and take your best shot. Good Luck!!

Key 1:
First reveal the shifted meaning, deep within Key two;
Then use the answer from before; you'll know what to do.
Then query them each yes or no by Eratosthenes;
Yes or no to zero through nine, the number that you need.

Key 2: '=' 852 , '?' 1 , '_' -200 , '8' 666 , '5' 8 , '6' 7 , '7' 109

Ex. Key 2: '8' 4523 , '=' 5 , '7' 51 , '5' 3 Ex. Answer=3

Answer from Previous Room:

29

The keypad has only digits. You can see some fingerprints on it, but only on two keys: 0 and Enter. There are scratch marks on the wall next to it that say "OH GOD THE ITCH!!!".

This room has now been solved. The next room can be found here

Answer 1

Is the answer

117?

Explanation:
First reveal the shifted meaning:

Replace the quoted character with the other from its key on a keyboard (toggling the shift key), giving + 852, / 1, - (-200), * 666, % 8, ^ 7, & 109 for the actual key 2 and * 4523, + 5, & 51, % 3 for the example.

Then use the answer from before:

Apply each stage's operator separately to 29 (the answer from before), interpreting % as modulus and & as bitwise AND to get 881, 29, 229, some big number, 5, another big number, 13 for the actual key and a big number, 32, 17, 2 for the example.

From there:

Proceed as in Anne's earlier answer, using each stage as a separate digit. For each digit, calculate if it is prime (1: yes, 0: no) (hint: Sieve of Eratosthenes), giving 1110101 for the actual answer and 0011 for the example, and convert from base 2 (yes or no) to base 10 (0 to 9), giving a final answer of 3 for the example and 117 for the actual key.

Note:

I didn't have to calculate the big numbers because they were either products of two numbers or powers of a number (therefore the product of multiple instances of the number) and were therefore not prime.

Answer 2

Okay, I'll give this a shot. Not too sure about it though.

First step: reveal the shifted meaning

I took the characters as ASCII numbers and shifted them by the number following it.
For example, '=' is 61 in ASCII, shifted by 852, gives 852+61 = 913. Doing all the same way gives the string: 913 64 -105 722 61 61 164

Use the answer from before:

Pretty unsure about this one, but I tried shifted each of these numbers by 29, but since 29 is the same as shifting by 3, I just added 3 to each. This gives 916 67 -102 725 64 64 167

Query yes or no by Eratosthenes:

He invented a method of finding primes, so I'll assign each number a 0 or 1 based on whether it's prime This gives 0 1 0 0 0 0 1

Yes or no to 0-9:

Just convert from binary to base 10. This gives an answer of 33

Works for the example key:

The string after the ASCII shift is 4579 66 106 56. Then the add 3 gives 4582 69 109 59. Yes-or-no for primes is 0 0 1 1, which is 3 in decimal