# [seqfan] Re: On a claim by Chun-Xuan Jiang.

Harvey P. Dale hpd1 at nyu.edu
Thu Mar 15 18:30:16 CET 2012

```	This Mma program generates the terms up to 100,000 in just over
one second:

Select[Range[100000],And@@PrimeQ/@(#{6,12,18,36,72}+1)&]

Best,

Harvey

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu
[mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Jack Brennen
Sent: Thursday, March 15, 2012 1:36 AM
To: lejeffery7 at gmail.com
Cc: Sequence Fanatics Discussion list
Subject: [seqfan] Re: On a claim by Chun-Xuan Jiang.

It's probably infinite, but a proof is probably beyond reach, I'm
guessing.

The sequence is not in the OEIS.  Values through 10^5:

1, 121, 380, 506, 511, 3796, 5875, 6006, 8976, 9025, 9186, 10920, 12245,
12896, 14476, 14800, 15386, 22451, 23471, 32326, 35175, 38460, 39536,
40420, 41456, 43430, 44415, 59901, 60076, 61341, 74676, 76615, 76986,
82530, 87390, 99486

On 3/14/2012 10:30 PM, Ed Jeffery wrote:
> Sorry to post again so soon.
>
> In his paper "Disproof of Reimann's Hypothesis," which is supposed to
> have appeared in Algebras, Groups and Geometries, Vol 21, 2004, see
> http://vixra.org/pdf/1004.0028v1.pdf (page 10), Chun-Xuan Jiang claims

> that there exist infinitely many integers k such that
>
> p1 = 6*k + 1,
> p2 = 12*k + 1,
> p3 = 18*k + 1,
> p4 = 36*k + 1,
> p5 = 72*k + 1,
>
> and p1, p2, p3, p4, p5 are all primes. The numbers n = p1*p2*p3*p4*p5
> are a class of so-called Carmichael numbers.
>
> I tried to calculate the sequence of such k manually but failed, since

> I don't have anything like Mathematica. It is obviously true for k =
> 1, but I got tired of checking for primality at around k = 85. So I
wonder:
>
> What are the next several values of k?
>
> Is the sequence indeed infinite?
>
> Is the sequence in the OEIS database?
>
> Regards.
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>

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