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April 16th, 2018, 10:14 AM   #1
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Prime or not ?

Is $\displaystyle 14n-3$ prime for each positive integer $\displaystyle n$
if so then how to prove it ?
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April 16th, 2018, 10:35 AM   #2
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$\dfrac{14n - 3}{3} = 14 * \dfrac{n}{3} - 1.$

Do you suppose there are some positive integers evenly divisible by 3?
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April 16th, 2018, 11:58 AM   #3
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It's easier to disprove it: 14 × 2 - 3 = 5², which is composite.

One can similarly deal with $14^n - 3$.
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April 16th, 2018, 02:19 PM   #4
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There is no simple polynomial formula for primes.
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April 16th, 2018, 05:35 PM   #5
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Where "simple" means what?
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April 16th, 2018, 09:34 PM   #6
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Quote:
Originally Posted by idontknow View Post
Is $\displaystyle 14n-3$ prime for each positive integer $\displaystyle n$
if so then how to prove it ?
So you did not even bother to check as far as $n=2$ before asking about this?
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April 16th, 2018, 11:29 PM   #7
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Quote:
Originally Posted by skipjack View Post
Where "simple" means what?
Any. Mathman meant to say that there is no polynomial that produces only primes. Simple or not. I think it was a rhetorical imprecision, not a mathematical one. There is no such thing as a simple polynomial, it's not a definition I've ever heard. So mathman was using simple as an intensifier ... a simple polynomial, as in a mere polynomial. No mere polynomial could do what you want. No simple polynomial etc.

That's how I interpreted mathman's remark. Simple as in a rhetorical flourish; not at all as specifying some subset of all the polynomials.
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Last edited by Maschke; April 16th, 2018 at 11:32 PM.
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April 17th, 2018, 12:46 PM   #8
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How can we show that the prime formula exists or not ?
In math we always must prove the existence first
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April 17th, 2018, 01:46 PM   #9
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Quote:
Originally Posted by mathman View Post
There is no simple polynomial formula for primes.
Polynomial with integer coefficients.
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