Re: New gigantic AP-4
- --- In firstname.lastname@example.org, "Jens Kruse Andersen"
> July 27 I wrote:
> > Congratulations to Jim Fougeron for
> > (18271126 + 9548007*n)*2^35000+1, n = 0..3 (10544 digits)
> > I saw it at http://primes.utm.edu/primes/status.php and have
> > http://hjem.get2net.dk/jka/math/aprecords.htmIndeed. Started just after Mike Oakes 10004 digit AP4 discovery in
> The current status page shows a 10043-digit AP4 by Ken Davis:
> (97070894 + 104086947*n)*2^33333+1, n=0..3
> It's the second largest known with unfortunate timing.
> The search probably started before Jim's discovery.
I've found 28000+ 100043 digit prp's so far
with 11000+ gigantic AP3's (Ap4 was found by extending one of these).
That along with my recent false CPAP4 has led me to believe that
Poisson doesn't like me. Never mind as you know from my 5132 digit
BLS CPAP3 I'm patient.
> Unlike most other prime searches, this cannot start overCongrats on these finds
> at another size without losing a lot more work than sieving.
> Congratulations anyway. Gigantic AP4's are impressive.
> I have set 3 easier records with prp tests by the GMP library:
> 69-digit AP14: (1067385825+193936257*n)*151#+1, n=0..13
> 29-digit AP17: (1259891250+70154768*n)*53#+1, n=0..16
> 29-digit AP18: (1051673535+32196596*n)*53#+1, n=0..17
> Jens Kruse Andersen
> Let puzzle(n) = sqrt(n)*(1 - log(n#)/n)http://mat.fc.ul.pt/ind/ncpereira/Bounds%20for%20Th,Ps,Ga,Ri.pdf
> Puzzle 1: Try to find a prime, p_min, such that
> puzzle(p_min) < puzzle(110102617)
> Puzzle 2: Try to find a prime, p_max, such that
> puzzle(p_max) > puzzle(19373)
And some further excursions of the related function: