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)
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)
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)
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.
(1+2)-1=2 and 1+2+3-1=5, sorry anyway, need to replace all s with t.
Yeah..I found out the proof too:) Quite easy though!
Therefore, the only twin prime for this generalize equation is (5,7).
Last edited by Stangerzv (2013-07-20 19:33:31)
The proof is as follows:
Which can be factorized as follows:
Which is a composite number.
Last edited by Stangerzv (2013-07-20 19:32:35)