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

[franktaw at netscape.net]

It would also imply that there are no prime gaps larger than 22; but it 
is easy to see that there are arbitrarily large prime gaps.

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Tue, May 13, 2014 8:13 am
Subject: [seqfan] Re: seq [1,5,7,11]


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,
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/