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#1 2013-04-15 14:32:05

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

What is the largest Twin Primes of this form you can get? Ver 3

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

, could be the only solution

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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#2 2013-04-16 13:30:20

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: What is the largest Twin Primes of this form you can get? Ver 3

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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#3 2013-04-17 11:17:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,840

Re: What is the largest Twin Primes of this form you can get? Ver 3

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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#4 2013-04-17 15:09:15

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: What is the largest Twin Primes of this form you can get? Ver 3

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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