Loading ...
Sorry, an error occurred while loading the content.

Missing the Point, the Table Might Help

Expand Messages
  • Milton Brown
    I am not sure why you are missing my point. But, I was not atempting to generator all twin primes, only to use them to prove that there are an infinite number.
    Message 1 of 2 , May 6, 2005
    • 0 Attachment
      I am not sure why you are missing my point.
      But, I was not atempting to generator all twin primes,
      only to use them to prove that there are an infinite number.

      So, I will use whatever twins I feel like.
      Perhaps you were misled by some more vocal people,
      who miss the point a lot; it doesn't matter.

      Don't take the liberty of modifying my material. Thank you!

      The rest of you might be interested in the following table:

      Least Twin Primes Past Factorial

      n, n!, n+1, length, least twin primes past factorial

      2 2 3 2 => (5, 7)
      3 6 4 4 => (11, 13)
      4 24 5 18 => (29, 31)
      5 120 6 96 => (137, 139)
      6 720 7 600 => (821, 823)
      7 5040 8 4320 => (5099, 5101)
      8 40320 9 39600 => (40427, 40429)
      9 362880 10 322560 => (362951, 362953)
      10 3628800 11 3265920 => (3629027, 3629029)

      11 39916800 12 36288000 => (39916817, 39916819)
      12 479001600 13 439084800 => (479001791, 479001793)

      +(5, 7)
      6+(5, 7)
      24+(5, 7)
      120+(17, 19) => (2*3!+5, 2*3!+7)
      720+(101, 103) => (4*4!+5, 4*4!+7)
      5040+(59, 61) => (2*4!+3!+5, 2*4!+3!+7)
      40320+(107, 109) => (4*4!+3!+5, 4*4!+3!+7)
      362880+(71, 73) => (2*4!+3*3!+5, 2*4!+3*3!+7)
      3628800+(227, 229) => (5!+4*4!+3!+5, 5!+4*4!+3!+7)

      39916800+(17,19) => (2*3!+5,2*3!+7)
      479001600+(191,193) => (5!+2*4!+3*3!+5,5!+2*4!+3*3!+7)

      2!
      3!+(5,7)
      4!+(5,7)
      5!+2*3!+(5,7)
      6!+4*4!+(5,7)
      7!+2*4!+3!+(5,7)
      8!+4*4!+3!+(5,7)
      9!+2*4!+3*3!+(5,7)
      10!+5!+4*4!+3!+(5,7)

      11!+2*3!+(5,7)
      12!+5!+2*4!+3*3!+(5,7)


      Still seems to be quite regular here.

      Milton L. Brown


      > [Original Message]
      > From: Mark Underwood <mark.underwood@...>
      > To: <primenumbers@yahoogroups.com>
      > Date: 5/6/2005 10:43:15 AM
      > Subject: [PrimeNumbers] Re: Infinite Number of Twin Primes
      >
      >
      > Jud's point is well taken. Milton's original offering was that twin
      > primes would be generated from only previously generated twin primes.
      >
      > I took the liberty to modify Milton's original offering to this:
      >
      > Starting with n=3 and (5,7) as the first twin prime pair, if we add
      > *or subtract* a (previously generated) twin prime pair from n! to
      > generate more twin prime pairs, how far can n go before there is a
      > failure to produce twins? Answer : n=22.
      >
      > But if instead of n! we use p#, then we can get as high as p = 61
      > before there is a failure to produce. (61 is the only prime to fail
      > before 103. After that failures become more common, as one might
      > expect.)
      >
      >
      > Mark
      >
      >
      > PS to certain others: Where is the love? How can there ever be peace
      > in the world if we respect our own knowledge or sensibilities or
      > tradition over our fellow human beings?
      >
      >
      >
      >
      >
      >
      >
      >
      > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      > The Prime Pages : http://www.primepages.org/
      >
      >
      > Yahoo! Groups Links
      >
      >
      >
      >
      >
    • Jud McCranie
      ... The main problem is that you haven t shown that for every n, there is an x such that n!+x and n!+x+2 are both primes. It doesn t really matter if x and
      Message 2 of 2 , May 7, 2005
      • 0 Attachment
        At 08:16 PM 5/6/2005, Milton Brown wrote:
        >I am not sure why you are missing my point.
        >But, I was not atempting to generator all twin primes,
        >only to use them to prove that there are an infinite number.
        >
        >So, I will use whatever twins I feel like.
        >Perhaps you were misled by some more vocal people,
        >who miss the point a lot; it doesn't matter.

        The main problem is that you haven't shown that for every n, there is an x
        such that n!+x and n!+x+2 are both primes. It doesn't really matter if x
        and x+2 are a pair of twin primes or not. Now, n!+x is more likely to be
        prime for small prime x than composite x, but that is it. You haven't
        shown that there must be an x that works for each n.
      Your message has been successfully submitted and would be delivered to recipients shortly.