## Re: [primeform] New gigantic AP-4

Expand Messages
• ... 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
Message 1 of 133 , Aug 15, 2007
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 updated
> http://hjem.get2net.dk/jka/math/aprecords.htm

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.
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
• ... http://mat.fc.ul.pt/ind/ncpereira/Bounds%20for%20Th,Ps,Ga,Ri.pdf And some further excursions of the related function:
Message 133 of 133 , May 15, 2010
> Let puzzle(n) = sqrt(n)*(1 - log(n#)/n)
>
> 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)

http://mat.fc.ul.pt/ind/ncpereira/Bounds%20for%20Th,Ps,Ga,Ri.pdf

And some further excursions of the related function:
http://www.primefan.ru/stuff/primes/table.html
Your message has been successfully submitted and would be delivered to recipients shortly.