NOTE: I am not an actual math pro and neither am studying some kind of advanced math. I just thought that in binary, the prime numbers might have something that could make It possible to find logic in It. Could be all in my head or just because binary is a simple logic system and I could be confusing things, but I wouldn't let It go if could be useful in some way.
I have put prime numbers from range 2-97 in binary form and tried to look for any logical form. It turns out that looks pretty random of course, but if this can contribute in the looking of prime logic(if there's any), I wouldn't just throw this in the trash.
here's what I did
2 = 0000010 - start after the number two
3 = 0000011 - 1 created
5 = 0000101 - 1 moved
7 = 0000111 - 2 created
11 = 0001011 - 1 moved
13 = 0001101 - 2 moved
17 = 0010001 - 1 + 2 = new house
19 = 0010011 - 3 created
23 = 0010111 - 3 moved, 4 created
29 = 0011101 - 3 and 4 moved
31 = 0011111 - 5 created
37 = 0100101 - new house, 5 moved
41 = 0101001 - 5 moved
43 = 0101011 - 6 created
47 = 0101111 - 6 moved, 7 created
53 = 0110101 - 7 moved, 6 + 5 = next house? !!!new thing happened, OR, maybe it happens after n amount of houses so maybe it's not creation but rather going to the next house!!!
59 = 0111011 - 7 moved, 8 created
61 = 0111101 - 8 moved
67 = 1000011 - all got used to create a new house, 9 created
71 = 1000111 - 9 moved, 10 created
73 = 1001001 - 9 + 10 = next house? !!!!!!!!!!!!!!!!!!
79 = 1001111 - created 11, moved 11, created 12
83 = 1010011 - they got used to create a new house(called 13) and 14 was created
89 = 1011001 - 14 moved 2 houses
97 = 1100001 - 14 + 13 = next house
result: It looks random when we make it like that. But If we look deeper It might make sense.
If this seems confusing(probably is), I added numbers as their names. I am not counting on the first 1(from right to left) because It will always be there and they could either be moving to the next house or adding each other to go to the next house. I hope you guys can understand with that info I gave...