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Primenumbers

Member

Registered: 2013-01-22

Posts: 149

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

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

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)

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