Re: [primeform] New gigantic AP-4
- July 27 I wrote:
> Congratulations to Jim Fougeron forThe current status page shows a 10043-digit AP4 by Ken Davis:
> (18271126 + 9548007*n)*2^35000+1, n = 0..3 (10544 digits)
> I saw it at http://primes.utm.edu/primes/status.php and have updated
(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.
Unlike most other prime searches, this cannot start over
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: