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Re: Three questions??

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  • nick_honolson
    ... problem ... chance in hell ... that will eventually be in reputable journals is first circulated by preprint; often on the Internet. Mathematicians often
    Message 1 of 5 , Mar 1, 2005
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      --- In primenumbers@yahoogroups.com, Chris Caldwell <caldwell@u...>
      wrote:
      > At 01:43 PM 2/27/2005, D├ęcio Luiz Gazzoni Filho wrote:
      > >> 2. Why do people choose to broadcast their solutions to this
      problem
      > >> on the internet?
      > >
      > >Beats me. But it makes no difference, because anyone who had a
      chance in hell
      >
      > Depends what you mean by broadcast. Virtually all mathematics
      that will eventually be in reputable journals is first circulated by
      preprint; often on the Internet. Mathematicians often say if you
      are waiting to read journals then you are two-years behind the
      current research.
      > Example: "Primes in P" was circulated on the net, gained
      acceptance,
      > was improved on repeatedly, all well before its first publication.
      >
      > You circulate in any media to share what you have. Often you get
      corrections
      > and suggestions. Sometimes references that you missed. (Amateurs
      > often miss the point of references--you must show you know how your
      > works fits in with the current literature.)
      >
      > But if instead you mean why do they have "Goldbach Proof" websites.
      > That is because no one would publish their trash. Audience is the
      > key--who are you writing to?

      I do hate to being called a crackpot by people who DON'T think what
      Chris is saying here is a good way to gain acceptance. I just wish
      there where more people who could help me when I have questions and
      willing to help me find the answers. For example I have recieved the
      following fowarded message which I can not answer. I wonder if any
      of you can. If not who and where can I ask?



      Can you answer the following?

      John

      ---------
      From: John W. Nicholson <reddwarf2956@...>
      To: caldwell@...
      Subject: Questions
      Sent: Friday, January 28, 2005 7:24 PM
      I have many question. ;-)

      On your page with Fortunate numbers:
      http://primes.utm.edu/glossary/page.php?sort=FortunateNumber

      Is there a term for prime numbers not in both Fortunate number and
      the
      Fortunate number list? I am thinking of calling them unfortunate
      prime numbers.
      Simular, but for primes that show up more than once, like 61 called
      very
      fortunate numbers. Are there an infinete number of both types?

      Is there a relationship between composite pair of p#+/-1 and the
      size of the
      gap mentioned? With both of these numbers composite there is a large
      gap
      between the less Fortunate number and the Fortunate number. How big
      is it?

      I know there is a relationship between the gap with p#+/-1 and the p!
      +/-1 gap.
      I mean if p#+/-1 is prime, then there is a gap >= the gap of size p.
      Because p!
      has a gap after p!+1 of at least p, realize that n!/n# = integer.
      And For any N, the sequence (N + 1)! + 2, (N + 1)! + 3, ..., (N +
      1)! + N + 1
      the gap is of size n.
      From: Paulo Ribenboim's book The Little Book of Big Primes. page 142

      In your paper on http://primes.utm.edu/references/refs.cgi?
      long=CG2000 states
      some proofs, namely theorems 2.4 and 2.5, which relates to p# or
      some number <
      p#, right? I mean there is a prime q which has the same congruences
      to p! as to
      p#.

      Can you state theorems 2.4 and 2.5 on web pages connected
      with "factorial
      primes"? You might want to link the primorial prime pages to it to
      the
      Fortunate numbers?

      Also, you might add to the page
      http://primes.utm.edu/glossary/page.php?sort=PrimeGaps a comment
      about the gap
      stated above. I know that it is not the smallest gap because 89 is
      the first
      the gap which follows the sum of two gaps larger than the n! gap.
      With "sum of
      two gaps" I mean while looking at largest number of the smallest
      factor of
      composites of the gap. This may sound confusing, so restating.

      For a gap, d, for a prime number p_n to p_(n+1), there are d numbers
      which are
      composite to primes smaller than p_n and p_(n+1). Each of these
      composites have
      a factor f_d which is the smallest factor. The largest f_d in the
      gap makes the
      final gap size d by summing the gap that was before and after. This
      was for the
      d after p_n there is another one for d before p_n too. Is there a
      previously
      stated gap function with these terms? If not, why not?

      More questions with http://primes.utm.edu/references/refs.cgi?
      long=CG2000

      In Theorem 2.4 is
      i) n divides 1!-1 and 0!-1
      Why is this statement needed? I mean (1!-1)/n = 0 and (0!-1)/n = 0,
      right?


      Table 4:
      1) What reason are the other primes < 499 not listed?
      2) Why are there pairs? (My guess is that there is a relationship
      with
      quadratic congruences.)
      3) Is there a proof which states that the individual pairing (the
      ones in
      which p = n - k -1) is always even-even or odd-odd but the total
      pairing does
      not have to be all even or all odd? Why are they not mixed?
      4) With my guess with quadratic congruences, what is relationship
      of the signs
      of the units added with quadratic congruences?
      5) No squares with pairings. Why? Also no n^m? Why, again?
      6) Is there a correlation between the factor and the sign of the
      unit?
      7) Is there a correlation between the factorial and the sign of the
      unit?
      8) Is there a correlation between the k value and the sign of the
      unit?
      9) Are there tables of factors of factorial numbers n!+/-1
      somewhere? (at
      least to 4000, to get pass the Wilson and Wieferich primes 563,
      1093, and 3511,
      with and without the pairing)
      10) With twins, how does the above questions relate?
      11) I see with 16!+1 both 137 and 139 are factors, does this mean
      anything with
      twins? What about 16!+1 pairs 120!-1 and 122!-1?
      12) I see with prime 61 both 16!+1 and 18!+1 are divisible
      factorials, does
      this mean anything with twins? Again, with the factorial pairs
      respectfully?
      13) What about with: Theorem: (Clement 1949)
      The integers n, n+2, form a pair of twin primes if and only if
      4[(n-1)!+1] = -n (mod n(n+2))?
      How about with this theorem with the theorems 2.4 and 2.5 and the
      one here
      http://www.primepuzzles.net/problems/prob_002.htm?

      From your page: http://primes.utm.edu/glossary/page.php?
      sort=TwinPrime and the
      book stated above too.
      14) What about Wilson primes, is there anything relating them to
      (mod n^2)?

      Can the theorem state in Q13) be combined with Proth's? Maybe some
      other prime test, like Fermat's little theorem or a strong psp test?

      Can you make a web page on the inclusion/exclusion principle
      relitive to primes? You could show why all attempts so far with the
      twin primes conjecture has failed.
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