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

A= 3, 15, 105, 1155, 15015 x next prime in the series................

p= prime or not factorable by any primes in A

and a gap of 4, therefore a gap of 4 can not occur because p+2 can not be prime

and a gap of 8, therefore a gap of 8 can not occur because p+2 can not be prime

Divide A by 3 and multiply by 2

another p

and a gap of 6, therefore a gap of 6 can not occur because p+2 can not be prime

Divide A by 5 and multiply by 2

another p

and a gap of 10, therefore a gap of 10 can not occur because p+2 can not be prime

**..........And so on until a gap that must be >2 becomes a gap that must be >infinity, there therefore must be an infinite No. of twin primes.**

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

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

**I realise my first post is incomplete so I have made some amendments...............**

A= 3, 15, 105, 1155, 15015 x next prime in the series................

p= prime or not factorable by any primes in A

and a gap of 2, therefore a p+1 can NOT be a prime because p+2 can not be prime

and a gap of 4, therefore a gap of 4 can not occur because p+2 can not be prime

OR and a gap of 4, therefore a gap of 4 can not occur because p+1 can not be prime

With a gap of 4, one number minused from A will be divisible by 4 or 2. If one is divisible by a higher than 4, the other can't be because the gap would have to be higher than 4 for the remainders to match. Therefore we can express a gap of 4 using the above equations, where if one number is divisible by a greater than 4 this will be p+1 an even no. and p is what was divisible by 4 but no higher.

and a gap of 8, therefore a gap of 8 can not occur because p+4 can not be prime

and a gap of 8, therefore a gap of 8 can not occur because p+2 can not be prime

and a gap of 8, therefore a gap of 8 can not occur because p+1 can not be prime

With a gap of 8, one number minused from A will be divisible by 2,4 or 8. If one is divisible by a higher than 8, the other can't be because the gap would have to be higher than 8 for the remainders to match. Therefore we can express a gap of 8 using the above equations, where if one number is divisible by a greater than 8 this will be p+1 an even no. and p is what is divisible by 8 but no higher.

Divide A by 3 and multiply by 2

another p

and a gap of 6, therefore a gap of 6 can not occur because p+2 can not be prime

With a gap of 6, one number minused from A will be divisible by 3. If one is divisible by a higher than 3, the other can't be because the gap would have to be higher than 6 for the remainders to match. Therefore we can express a gap of 6 using the above equation, where if one number is divisible by a greater than 3 this will be p+2 and p is what is divisible by 3 but no higher.

Divide A by 5 and multiply by 2

another p

and a gap of 10, therefore a gap of 10 can not occur because p+2 can not be prime

With a gap of 10, one number minused from A will be divisible by 5. If one is divisible by a higher than 5, the other can't be because the gap would have to be higher than 10 for the remainders to match. Therefore we can express a gap of 10 using the above equations, where if one number is divisible by a greater than 5 this will be p+2 and p is what is divisible by 5 but no higher.

**..........And so on until a gap that must be >2 becomes a gap that must be >infinity, there therefore must be an infinite No. of twin primes.**

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

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