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

You are not logged in.

#1 2013-07-20 16:44:51

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

My New Primes with a Strange Property

Consider these two equation:

There are plenty of Primes of this form:

But there is no prime of this form:

If you could find a prime then you must be kool:) If you could find one, n should be greater than at least 100,000.

If you could find a counterexample then it would be a pleasure to see if you could find the twin primes of the form as follows:

Last edited by Stangerzv (2013-07-20 18:52:32)

Offline

#2 2013-07-20 16:55:54

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

Re: My New Primes with a Strange Property

The Generalize equation can be written as follows:

I do believe it would behave more less the same for all t>1

Last edited by Stangerzv (2013-07-20 21:25:13)

Offline

#3 2013-07-20 17:13:15

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

Re: My New Primes with a Strange Property

For t=1,

There are plenty of Prime of this form.

But for this equation:

There are only two primes for n<1,000,000 (i.e. 2 & 5)

Last edited by Stangerzv (2013-07-20 18:53:08)

Offline

#4 2013-07-20 18:06:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: My New Primes with a Strange Property

Hi;

P5 is not a prime. And n=2 is the only possible prime! The proof is quite easy.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#5 2013-07-20 18:52:01

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

Re: My New Primes with a Strange Property

Hi bobbym

(1+2)-1=2 and 1+2+3-1=5, sorry anyway, need to replace all s with t.

Offline

#6 2013-07-20 19:01:48

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

Re: My New Primes with a Strange Property

Yeah..I found out the proof too:) Quite easy though!

Offline

#7 2013-07-20 19:08:57

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

Re: My New Primes with a Strange Property

Therefore, the only twin prime for this generalize equation is (5,7).

Last edited by Stangerzv (2013-07-20 19:33:31)

Offline

#8 2013-07-20 19:26:52

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

Re: My New Primes with a Strange Property

The proof is as follows:

Since

Then

=>

Which can be factorized as follows:

Which is a composite number.

Last edited by Stangerzv (2013-07-20 19:32:35)

Offline

#9 2013-07-20 21:26:26

Stangerzv
Member
Registered: 2012-01-30
Posts: 181

Re: My New Primes with a Strange Property

Primes only occur at even t of the form 2^a for

where a is an integer

Last edited by Stangerzv (2013-07-20 22:22:10)

Offline

Board footer

Powered by FluxBB