Is it possible to prove, that the difference of two prime numbers, of which the first is precedessor and the next is follower in the "serie" of prime numbers is coming nearer the infinite when the greatness of the numbers is coming nearer the infinite?
prime numbers
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Vanhimmat
yes
It has been proved that there are infinitely many twin primes (primes a and b with a difference 2, i.e., a - b = 2).
Proof of the Twin Primes Conjecture Using Euclid's Logic:
Suppose that i(1)=i(2)=i(3) . . . =i(r)=2 are all the twin prime intervals. Let I(r)=2^r 1, i(r 1)=2 and I(r 1)=2^(r 1) 1 from which it follows that 2I(r)=I(r 1) 1. For all values of r, since interval i(r 1) divides 2I(r) (without dividing I(r) and I(r 1),) it is yet another interval and intervals i(1)=i(2)=i(3)= . . . =i(r) are not all the twin prime intervals, i.e., r->infinite in i(1)=i(2)=i(3)= . . . =i(r)=2.
The existence of infinitely many twin primes is still a conjecture, even though there seems to be a lot of evidence supporting it.
(Your proof also needs some changes, I'm afraid...)