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• ## Re: [PrimeNumbers] Re: Arithmetic progression

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• ... 40 digits!?!?!?! What s wrong with x^2+x+1077881853647981 ? x^2+x+5565451343405111 has no factors under 250.
Message 1 of 8 , Apr 2, 2002
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--- mbhawkuk <mdb36@...> wrote:
> > > Now I wish look for the a such that x^2-x+a all are prime
> for
> > > x=0,1,2,...,k, and k>41
> >
> > Yup, OK, I wasn;t too concerned with hunting for the primes that
> > time. However others were, and are. I beleive that there are
> people
> > who are using the ultra-dense QPs defined on by the A values on
> that
> > page in order to find runs of primes.
>
> If people are interested in these forms and the ultra-dense
> sequences
> you can produce, take a look at the archives of the primeform
> group,
> messages 658, 667, 684 and replies to them go into this in quite a
> lot
> of detail. For a taster - the form
> (n*101*103*107*127*157*197)^2+(n*101*103*107*127*157*197)+398878547
> has no factors < 200 for any n, and has only ~40 digits, compared
> to
> the 82 digits of the k.199#+1 form. The disadvantage is that it is
> time consuming to find these forms, and also time consuming to
> prove
> primality.

40 digits!?!?!?!
What's wrong with x^2+x+1077881853647981 ?
x^2+x+5565451343405111 has no factors under 250.

http://www.primepuzzles.net/conjectures/conj_017.htm

> At one stage I was considering attempting to find an ultra dense
> triplet region in order to have an easy way to break the triplet
> record, unfortunately that is very difficult and I didn't ever find
> anything useful. The other disadvantage is you end up with numbers
> with no short form, which are generally discouraged from the prime
> pages database.

Not discouraged really, simply much less convenient.

Phil

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• ... ok ok - it was just an example, there are much larger ones - it was the first one I made when I started investigating 2 and a half years ago :-) Michael.
Message 2 of 8 , Apr 2, 2002
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> 40 digits!?!?!?!
> What's wrong with x^2+x+1077881853647981 ?
> x^2+x+5565451343405111 has no factors under 250.

ok ok - it was just an example, there are much larger ones - it was the
first one I made when I started investigating 2 and a half years ago :-)

Michael.
• ... Dear Michael: Thank you very much for your direction. I need the practical number a such that x^2-x+a all are prime for x=0,1,2,...,k, and k 41 or up
Message 3 of 8 , Apr 3, 2002
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"mbhawkuk" <mdb36@...>wrote:

> > > Now I wish look for the a such that x^2-x+a all are prime for
> > > x=0,1,2,...,k, and k>41
> >
> > Yup, OK, I wasn;t too concerned with hunting for the primes that
> > time. However others were, and are. I beleive that there are people
> > who are using the ultra-dense QPs defined on by the A values on that
> > page in order to find runs of primes.
>
> If people are interested in these forms and the ultra-dense sequences
> you can produce, take a look at the archives of the primeform group,
> messages 658, 667, 684 and replies to them go into this in quite a lot
> of detail. For a taster - the form
> (n*101*103*107*127*157*197)^2+(n*101*103*107*127*157*197)+398878547
> has no factors < 200 for any n, and has only ~40 digits, compared to
> the 82 digits of the k.199#+1 form. The disadvantage is that it is
> time consuming to find these forms, and also time consuming to prove
> primality.
> At one stage I was considering attempting to find an ultra dense
> triplet region in order to have an easy way to break the triplet
> record, unfortunately that is very difficult and I didn't ever find
> anything useful. The other disadvantage is you end up with numbers
> with no short form, which are generally discouraged from the prime
> pages database.
>
> Michael.

Dear Michael:
Thank you very much for your direction.
I need the practical number a such that x^2-x+a all are prime for x=0,1,2,...,k, and k>41 or up the
larger number c , there is no such a.
My PC very poor, and sorry, I do't know the program.
In theory my recursive formula Tn is a functionall algorithm, it can become a program. although like
Phil said Not discouraged really, simply much less convenient.
I had submited my k-tuple prime conjecture to the Journal of number theory, if ,felicity, it is accepted,
I will quote above date, at least the date shall publish in the
http://www.primepuzzles.net/conjectures/conj_003.htm