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Re: [PrimeNumbers] Re: Arithmetic progression

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  • Michael Bell
    ... 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 1 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.
    • liufs
      ... 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 2 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
        Please anyone help me.

        China
        Liu Fengsui
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