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25075Re: [PrimeNumbers] Check guess, please (simultaneous primes in sequence)

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  • James Merickel
    May 19, 2013
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      Jens Kruse Andersen produced the 16th term of a sequence I requested and some sequence material to the side (of that term) as well as an advance of the 'Prime Curio!' submission I remarked on.  None of this have I checked, but I will note that he states a skip to a coincidence, where the curio submission is related..{16 follows 13, while Jens produces a case with prime for both signs of 17 in regards to expanding upon my submission}.
       
      Okay, I have the first 17 terms (of the sequence I was bringing up and that was clarified formally by Jens) and would say -- it seems to me -- that I was right for the wrong reason (a kind of double or multiple statistical error where I was expecting a larger 16th term, as my guess, than received (hence, 'seems' (?))).  The 17th term is 7504141544, so the ratio of the 16th to the largest term to that point (100215214829, the 13th) is merely greater than 8, and the drop 16th to 17th corresponds to a ratio of around 1/11.  I was in such a fog (or working as a non-mathematician) that I thought order-of-magnitude changes were expected in a more pronounced manner (This is not difficult to see as wrong). 
       
      Terms are {4650977, 4591226, 293937092, 10213103, 672582761, 1028570633, 1603407584, 2938481003, 3745479200, 25568575163, 16614925457, 19583366942, 100215214829, 84330274808, 55362283208, 827942544791, 7504141544, ...} [This is as far as I have it, and the first term still surprises me.]
       

      --- On Sat, 5/18/13, James Merickel <moralforce120@...> wrote:


      From: James Merickel <moralforce120@...>
      Subject: Re: [PrimeNumbers] Check guess, please (simultaneous primes in sequence)
      To: primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...>
      Date: Saturday, May 18, 2013, 7:14 PM



       



      At a better time, this would be or would have been a good (relative) time to advance a statistical partial definition of how much of a coincidence this is among a certain class of sequences (while advancing my knowledge of statistics). 
       
      At present, I would be over-Solomonizing my own mind, however, to attempt that (if you can see what that means locally).  
       
      Such would be unwise (but I'd like to consider you my oldest cousin, with no desired disregard for my immediate family (It seems like it seams right, because of one A.L., and not addressing this specifically leaves another A.L. still)). 
       
      James

      --- On Fri, 5/17/13, Jens Kruse Andersen <jens.k.a@...> wrote:

      From: Jens Kruse Andersen <jens.k.a@...>
      Subject: Re: [PrimeNumbers] Check guess, please (simultaneous primes in sequence)
      To: primenumbers@yahoogroups.com
      Date: Friday, May 17, 2013, 6:45 PM

       

      James Merickel wrote:
      > I don't have the first 15 terms with me, but THEY are easy
      > [The first collection of] 8 simultaneous primes are to be found
      > by adding/subtracting 1, 2, 4 and 5 to a (the sequence's) value,
      > multiplying by a power of 10 and adding 1.

      (827942544791 +/- n)*10^16+1 is prime for n = 1, 2, 4, 5

      827942544791 is the first solution. It did come later than expected.
      This seems like a coincidence. The next solutions are:
      1028465717858, 1086965448791, 1562679711122, 1609404153257, 1800846280763

      > {I also happen to have submitted to 'Prime Curios!' the value for
      > 12 simultaneous and the power is 1 (where 8 and 10 are added to
      > the list. ... A next step would be adding/subtracting 13.}

      (9477895607701082 +/- n)*10+1 is prime for n = 1, 2, 4, 5, 8, 10, 13
      This is the smallest solution. It also gives primes for n = 17.

      --
      Jens Kruse Andersen

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