The problem of testing primality can be expressed by the language LP consisting of all binary strings whose values as a binary number is prime. That is, given a string of 0's and 1's, say "yes" if the string is the binary representation of a prime and say "no" if not. For some strings, this decision is easy. For instance, 0011101 cannot be the representation of a prime, for the simple reason that every integer except 0 has a binary representation that begins with 1. However, it is less obvious whether the string 11101 belongs to LP, so any solution to this problem will have to use significant computational resources of some kind: time and/or space, for example.
I didn't understand why 0011101 can't be representation of prime.