Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 252

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)*

Offline

**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 252

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)*

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

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)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 252

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?

Offline