[seqfan] Re: A061421

[Georgi Guninski]

On Thu, Dec 06, 2012 at 10:43:44AM -0800, israel at math.ubc.ca wrote:
> 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
>


Looks like pari is faster for pseudo primality:
? n=4^33478-33478-1;
? ispseudoprime(n,3)
%2 = 1
? ##
  ***   last result computed in 5mn, 31,080 ms.
? ? ispseudoprime 
ispseudoprime(x,{n}): true(1) if x is a strong pseudoprime, false(0) if not. 
If n is 0 or omitted, use BPSW test, otherwise use strong Rabin-Miller test 
for n randomly chosen bases.