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

#1 2013-04-16 12:32:05

Stangerzv
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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 (2013-04-17 20:38:29)

#2 2013-04-17 11:30:20

Stangerzv
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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 (2013-04-17 17:42:28)

#3 2013-04-18 09:17:17

anonimnystefy
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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 (2013-04-18 09:20:53)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
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#4 2013-04-18 13:09:15

Stangerzv
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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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