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.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
(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)