# [seqfan] Re: (3^n+1)/2 is prime, A171381

Georgi Guninski guninski at guninski.com
Mon Jun 14 14:23:30 CEST 2010

```16,17,18 failed the pari pseudoprime test in less than 2 hours.

This seems to leave the smallest candidates:
20 - 0.5 million decimal digits
22 - 2 million decimal digits

Looks like the scientific approach is first to run P-1 or EC factoring (probably gmp-ecm) before pseudoprime tests. Have no idea how long the pseudoprime test will take.

On Mon, Jun 14, 2010 at 12:57:08AM -0400, Maximilian Hasler wrote:
> On Sun, Jun 13, 2010 at 7:31 AM, Georgi Guninski <guninski at guninski.com> wrote:
> > On Sun, Jun 13, 2010 at 01:24:58AM -0400, N. J. A. Sloane wrote:
> >> %E A171381 Incorrect terms a(7)-a(15) deleted Jun 12 2010 by Jon Schoenfield
> >> (or in other words, 0,1,2,4,5,6,>=15)
> >> Can anyone find the next term?
> >
> > 2^{15,16,17,18} are not in the sequence
>
> More terms not in the sequence, because
> (3^(2^m)+1)/2  is divisible by  1+2^(m+1)*q :
>
> [m,q] =
> [3, 1]
> [7, 1]
> [8, 24]
> [10, 29]
> [11, 193]
> [15, 1]
> [19, 13]
> [21, 37]
> [26, 24]
> [28, 23]
> [29, 72]
> [31, 1080]
> [32, 24]
> [34, 1469]
> [36, 6630]
> [38, 12]
> [39, 42]
> [44, 443]
> [45, 228]
> [49, 7]
> [51, 198]
> [54, 5]
> [56, 2460]
> [60, 3810]
> [61, 18]
> [63, 12]
> [64, 36]
> [72, 804]
>
> Maximilian
>
>
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