[seqfan] Re: On a claim by Chun-Xuan Jiang.
Jack Brennen
jfb at brennen.net
Thu Mar 15 06:35:39 CET 2012
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.
>
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