If I am interpreting correctly, here is a verbal translation of your examples:
Eleven is prime. In binary 11 is 3 which is also prime.
One Hundred One is prime. In binary, 101 is 5 which is also prime.
One Hundred One Thousand One Hundred Eleven is prime and so is the binary equivalent of 47.
Given that the number of primes is proven infinite, a corollary would be that an infinite number of decimal/binary pairs should also exist.
Note the distribution curve if you graph the examples. Thats a kind of unique pattern.
Fusion
