Re: [PrimeNumbers] Re: Carmichael question
- The website richard made reference to lists all Carmichaels under 10^16
listed and all 3-Carmichaels < 10^18 listed.
richard_heylen would it be possible for us to see your code? I can throw
a few fast machines at this for a while...
At 05:54 PM 11/2/2002 +0000, paulunderwooduk wrote:
>--- In primenumbers@y..., "richard_heylen" <richard_heylen@y...>
> > It's all rather hand-
> > wavey and the implementation sucks but it trots out the Carmichaels
> > everyone else has found, in a couple of minutes on a P3-800.
>Are your methods transferable to n^3-n-1? If so, how long would it
>take to do to n=10^13 or n=10^14 in this case?
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- Apologies for the aborted attempt at a post. 'Tab' followed by either
'space' or 'return' (too quick to know what happened) seems to be a
lethal key combination.
From: "mcnamara_gio" <mcnamara_gio@...>
>2, 3, and 5 can never be factors. This boosts density by a factor of
> What do you think about this sequence a(n)=n^2+7n-1. Its terms are
> usually prime. I have calculated that 72% of a(n) so that n<500 is
> prime. 81% of a(n) is prime when n<5000. 85.6% of a(n) is prime when
> n<50000 and 88.5% of a(n) is prime when n<500000. I am going to find
> more prime terms in this sequence. What do you think about it?
(2/1)*(3/2)*(5/4) over arbitrary ranges. However, 7,11, 13 and 17 both
divide 2 of the p possible residues. This decreases density by a factor
of (5/6)*(9/10)*(11/12)*(15/16) over arbitrary ranges.
Looking at primes up to 10000, the density boost is almost exactly 2.75.
This is pretty feeble compared with Euler's famous trinomials.
Run this script in Pari/GP:
"rthis" "rnorm" "roots))
Research the Euler trinomials, and try the above script on them too, to see why
I say 2.75 is pretty feeble.
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