Re: [PrimeNumbers] Digits strings for prime numbers
- Regarding the possibility of an infinite string of binary digits,
which contains an infinite number of '1' digits, and which
yields only a single two-bit prime among all leading substrings...
This is easy to prove existence.
Effectively, one needs only to prove that for any integer k, there is
a composite number of the form k*2^n+1, for some n>=1.
Such a proof is easy:
Let A=k*2^n+1. If A is composite, we're done. So assume A is prime.
Let x be the order of 2 mod A.
Let B=k*2^(n+x)+1. B is divisible by A, and is thus composite.