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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

The generalized twin prime can be formulated as follows:

or

Where all Pn are consecutive primes and Ps is the resulting primes.

Example:

For P1=5, there would be no twin prime existed

For P1=7

and as P1>7, there is no twin prime numbers could be formed (A conjecture).

*Last edited by Stangerzv (2013-04-16 22:38:29)*

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

I think I had to retract the conjecture as there are many counter-examples:

However, once P1 becomes larger, this type of prime would become hard to find or simply non-exist.

*Last edited by Stangerzv (2013-04-16 19:42:28)*

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Were you just guessing that there are no twin primes for P1=5, cause it is a good one and a true one!

What's even more interesting is that there are no such pairs for any P1 of the form 3n+2.

*Last edited by anonimnystefy (2013-04-17 11:20:53)*

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

I just knew there is no solution as the multiplication got bigger, if there is a solution for primes, they usually occur at the smaller amount. It is interesting to know that there is no solution for 3n+1 but proving it would be a headache..I guess. How do you know it? You guessed?

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