20190406, 13:58  #12 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{5}×3×101 Posts 
... or Cain prize.

20190413, 16:10  #13 
Mar 2019
5·11 Posts 
What if I do a proof like this?
If the set of twin prime numbers is finite then we can make a list, let S be the list of twin prime numbers, S=P1,P2,P3,P4,PN Now let us construct a number Q such that Q=P1×P2×P3×P4×PN+1 If Q is a twin prime then there exists a larger twin prime then on S If Q is composite then non of the twin primes of S will divide Q. Both of this conclusions yield to a contradiction, therefore there are infinitely many twin prime numbers 
20190413, 16:55  #14  
"Curtis"
Feb 2005
Riverside, CA
2×3^{2}×7×41 Posts 
Quote:


20190414, 11:57  #15 
Mar 2019
55_{10} Posts 
Instead of the sum of the first n natural and twin primes numbers I correct it into an infinite sum of natural numbers and twin prime numbers

20190414, 12:00  #16 
Mar 2019
55_{10} Posts 
The contradiction of Q being composite is that it would not be divisible by any elemet of S because it always leaves remainder 1

20190414, 18:03  #17 
"William"
May 2003
New Haven
100101000001_{2} Posts 

20190415, 13:03  #18 
Mar 2019
5×11 Posts 
Clearly Q is larger than any other twin prime, so it does not equal one of them, since P1,P2,P3,P4...Pn constitute all twin primes Q can not be a twin prime. Thus it most be divisible by at least one of our finitely many twin primes, say Pk ( 1 less than or equal to k less than or equal to n) But when we divide Q by Pk we have a remainder of 1. This is a contradiction so our original assumption that there are finitely many twin prime must be false.

20190415, 13:06  #19 
Mar 2019
5·11 Posts 
I don't think so because the proof has a lot of mistakes that I have not been capable of solving

20190415, 13:26  #20  
"William"
May 2003
New Haven
100101000001_{2} Posts 
Quote:
But I lost you here, There are lots of primes that are not twin primes. Why is it impossible that Q is a product of only these nontwin primes? 

20190415, 13:34  #21 
Mar 2019
110111_{2} Posts 
It is impossible because we constructed an arbitrary number Q which is the product of the finite list of the twin primes and adding 1 to the product

20190415, 13:39  #22  
Mar 2019
5·11 Posts 
Quote:


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