[seqfan] Re: seq [1,5,7,11]

Charles Greathouse charles.greathouse at case.edu
Tue May 13 15:12:39 CEST 2014


This conjecture implies that there are at least x/12 - 1 primes up to x,
which contradicts the Prime Number Theorem.

The first counterexample is 44*12 = 528.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Sun, May 11, 2014 at 8:07 AM, Tw Mike <mt.kongtong at gmail.com> wrote:

> Dear seq fans,
>
> i'm trying submit seq [1,5,7,11] to OEIS.
> Seq [1,5,7,11]: it is conjectured that any nonnegative integer multiply by
> 12 then add one of the numbers must get at least a prime except 3.
>
> Let's take a random number 365 for test:
>
> ?isprime(12∗365+1)
> %1=0
> ?isprime(12∗365+5)
> %2=0
> ?isprime(12∗365+7)
> %3=0
>
> Is this correct? Here's one more test:
>
> ?isprime(12∗365+11)%4=1
>
> Any check,test,edit,suggestion, theory,clue,research are welcomed.
>
> Yours mike,
>
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>



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