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#1 2015-07-19 02:32:32

Primenumbers
Member
Registered: 2013-01-22
Posts: 131

Proof that there are an infinite number of twin primes attempt 2.

There are no more twin primes after prime, z.
A=3*5*7*11*13*17*19*23*29*31....................................*z

+/-
  where p and m are primes>z or =1


so long as
   or   
  whichever is greater rd. dwn. to nearest prime = z or less

+/-
must exist in the correct range otherwise m+/-1=
*composite then in a gap of 4 there are no more even no.'s left to
as m+1=
*composite and m+4-1=
*composite
Therefore some gaps must be >4. In these gaps we now know m+/-3=
*composite therefore these gaps must be >6 as m+1=
*composite m+3=
*composite and m+6-1=
*composite.
Still no even no.'s left for
.
And so on until gaps that must be >2 become gaps that must be >infinity.

Last edited by Primenumbers (2015-07-20 22:41:08)


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#2 2015-07-22 02:38:43

Primenumbers
Member
Registered: 2013-01-22
Posts: 131

Re: Proof that there are an infinite number of twin primes attempt 2.

Simpler version
There are no more primes after prime, z.
A=3*5*7*11*13*17*19*23*29*31............................................*z.
p= No. not factorable by any primes in A or 2.
p+/-1=

otherwise A - 2p and A- 2p +/-2= twin primes.
Some gaps must be >4 as p+1 and p+4-1=
.
No room for
.
These gaps must be >6 as p+1 and p+3 and p+6-1=
.
Again no room for
.
And so on until gaps that must be >2 become gaps that must be >infinity.

Last edited by Primenumbers (2015-07-22 02:40:38)


"Time not important. Only life important." - The Fifth Element 1997

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