Chatroom - 2019-11-07

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user433813

12:18 PM

How large can $\{c_{i,1}+2,...,c_{i,m(e_i)}+2\}$ be?

user433813

12:34 PM

That seems unimportant, only the size of $C(e_1)=\{2e_1-q_1,...,2e_1-q_{m(e_1)}\}$ seems relevant.

user433813

So, can $C(e_1)=\{2e_1-q_1,...,2e_1-q_{m(e_1)}\}$ be absolutely bounded?

user433813

1:03 PM

Goldbach's conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states: Every even integer greater than 2 can be expressed as the sum of two primes.The conjecture has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable effort. == Goldbach number == A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes. Since 4 is the only even number greater than 2 that requires the even prime 2 in order to be written as the sum of two primes, another form of t...

user433813

1:43 PM

Okay, so if a shift $\{c_1,..,.c_{m(a)}\} \to \{c_1+2,...,c_{m(a)}+2\}$ produces at least one prime, then it seems that GTC´s do not exist.

user433813

But even if that´s proven, much counterexamples could, at least conjecturally, exist.

user433813

Even if I prove that $m(a)<m(a+1)$, is anything crucial established then?

user433813

1:58 PM

It seems plausible that cardinality is much important and not the position of GTC´s if they are "far".

user433813

Typo, GCC´s.

user433813

But would that be stronger than the conjecture itself?

user433813

Well, depends on the precise formulation.

user433813

So GTC´s are not at all important, they are irrelevant.

user433813

2:16 PM

Also, the conclusion seems to be independent on whether $2w$ is GCC or not.

user433813

So, a more general statement than Goldbach´s conjecture should (could?) be true.

user433813

That one also seems possible to be generalized further, but that one even more general could be too hard for even an attempt of a solution.

user433813

3:04 PM

@Peter Why are you interested in Goldbach´s conjecture?

Peter

3:21 PM

I just looked at the different chat-rooms. Goldbach's conjecture is amazing ! Almost surely true, but apparently out of reach to prove. A statement stronger than this conjecture therefore is very unlikely to be solved. Try a statement somewhat weaker than Goldbach.

By the way, how did you arrive at the (possible) divisor 9091 of 10^100+9^9 ? Which software did you use ?

user433813

None, I just transformed the expression 10^100+9^9 into something else with basic laws of powers and elementary algebra on a paper.

user433813

3:59 PM

I think I obtained 10^100+9^9=a+b and b had a factor 9091, so if that would be also a factor of a then it would be a factor of 10^100+9^9.

user433813

22277 could be checked also.

user433813

4:14 PM

@AkivaWeinberger Hey.