[seqfan] Re: A061421

[israel at math.ubc.ca]

On Dec 6 2012, Georgi Guninski wrote:

>On Sun, Dec 02, 2012 at 08:35:57PM +0400, юрий герасимов wrote:
>> 
>> Dear SegFans, If A061421 Primes of the form 2^n + n + 1 : 2, 7, 71, 
>> 110427941548649020598956093796432407239217743554726184882600387580788973, 
>> a(5) = 2^1884 + 1884 + 1,.., these A_____? Primes of the form 4^n - n - 
>> 1 : 2, 13, 251, 4294967279, a(5) = ? Regards, Juri-Stepan Gerasimov.
>>
>
>For computations like this, OpenPFGW is your friend:
>
>$egrep 'PRP|prime' /tmp/pri1.log 
>4^1-1-1 is trivially prime!: 2
>4^2-2-1 is trivially prime!: 13
>4^4-4-1 is trivially prime!: 251
>4^16-16-1 is trivially prime!: 4294967279
>4^944-944-1 is 3-PRP! (0.0039s+0.0942s)
>4^33478-33478-1 is 3-PRP! (8.5771s+1.3188s)
>
>
>According to pari n=944 is pseudoprime.

Maple's "isprime" reports 4^944-944-1 as (very probably) prime.
This does one strong pseudo-primality test and one Lucas test.
It's still working on 4^33478-33478-1.

Robert Israel
University of British Columbia