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## 25566Re: [PrimeNumbers] re: Divisibility of the Sum of Two Prime Terms of Arithmeticlal Progre ssions

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• Jun 24, 2014
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Bill,
Here is statement "Two":

"Two, If an even positive integer N is not divisible by 4 and not divisible by 6, then it is not divisible by any twin prime middle number, and it is always equal to the sum of 2 twins, both being either small or large twins."

David is correct to say that 94 is a counterexample. It is an even positive integer not divisible by 4 and not divisible by 6.  It is not divisible by any twin prime middle number (as you point out), however, it is not equal to the sum of 2 twins.  Statement "Two" claims that is will be equal to the sum of 2 twins, therefore it is a counterexample.

Tom

On Tue, Jun 24, 2014 at 10:55 AM, 'w_sindelar@...' w_sindelar@... [primenumbers] wrote:
Re: Divisibility of the Sum of Two Prime Terms of Arithmetical Progressions

David, none of the counterexamples you cite in your message 25561, as refuting statement two of message 25560, are divisible by a twin prime middle number.

For example, 94 is not divisible by the middles 4, 6, 12, 18, 30, 42, 72.

I take this opportunity to add another property to the 2 statements.

Please append the phrase “and it always divides a twin prime middle number, a twin prime middle number of times” to the end of both statements.

Thank you.

Bill Sindela
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