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16442Re: Dat Dastardly 788 : (Now a stronger GC)

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  • John W. Nicholson
    Apr 14 8:09 PM
      One more thing, the gap are added or subtracted from the number
      below until there are to primes at the ends.

      89 (-7) ((96)) (+1) 97 (+4) 101 (+2) 103
      103-89 = 14
      96 +/- 7

      383 (-6) 389 (-8) 397 (-4) 401 (-1) ((402)) (+7) 409 (+10) 419 (+2)
      421
      421 - 383 = 38
      402 +/- 19

      509 (-7) ((516)) (+5) 521 (+2) 523
      523 - 507 = 14
      516 +/- 7

      761 (-8) 769 (-4) 773 (-13) ((786)) (+1) 787 (+10) 797 (+12) 809
      (+2) 811
      811- 761 = 50
      786 +/- 25

      883 (-4) 887 (-19) ((906)) (+1) 907 (+4) 911 (+8) 919 (+10) 929
      929 - 883 = 46
      906 +/- 23

      1109 (-7) ((1116)) (+1) 1117 (+6) 1123
      1123 – 1109 = 14
      1116 +/- 7

      1129 (-17) ((1146)) (+5) 1151 (+2) 1153 (+10) 1163
      1163 – 1129 = 34
      1146 +/- 17

      1249 (-10)1259 (-7) ((1266)) (+11) 1277 (+2) 1279 (+4) 1283
      1283 -1249 = 34
      1266 +/- 17

      1303 (-4)1307 (-12) 1319 (-2) 1321 (-6) 1327 (-29) ((1356)) (+5)
      1361 (+6) 1367 (+6) 1373 (+8) 1381 (+18) 1399 (+10) 1409
      1406 – 1303 = 106
      1356 +/- 53

      3221 (-8) 3229 (-17) ((3246)) (+5) 3251 (+2) 3253 (+4) 3257 (+2)
      3259 (+12) 3271
      3271 – 3221 = 50
      3246 +/- 25

      4201 (-5) ((4206)) (+5) 4211
      4211 – 4201 = 10
      4206 +/- 5


      John


      --- In primenumbers@yahoogroups.com, "John W. Nicholson"
      <reddwarf2956@y...> wrote:
      >
      > I have been looking at this paper of Harvey's. I think I have
      > discovered a few things which are very interesting. First let me
      > list the numbers which he found not to be middle numbers < 2*10^10:
      >
      > N = 96, 402, 516, 786, 906, 1116, 1146, 1266, 1356, 3246, and 4206.
      >
      > Harvey stated to me the correction of 4208 should be 4206.
      >
      > Note that all except the second one, 402, is == 1 (mod 5). Also as
      > would be expected all are divisible by 6, but they are a complete
      > residue set with (mod 4) == (mod 24) (I might be stating this
      wrong,
      > so let me restate this when divided by 24 the remainder is one of
      > 0,1,2, or 3.) There is only one of these with == 0 (mod 24),
      namely
      > 96. There is also a interesting thing with (mod 11) and N/6 ==
      (mod
      > 11) most have a factor of 2 except the first three. I did look at
      > (mod 7). There are no == 1,4 (mod 7). I wonder how this fits with
      > http://primepuzzles.net/problems/prob_003.htm ?
      >
      > N, (mod 11), N/6 == (mod 11), (mod 7)
      > 96, 8, 5, 5
      > 402, 6, 1, 3
      > 516, 10, 9, 5
      > 786, 5, 10, 2
      > 906, 4, 8, 3
      > 1116, 5, 10, 3
      > 1146, 2, 4, 5
      > 1266, 1, 2, 6
      > 1356, 3, 6, 5
      > 3246, 1, 2, 5
      > 4206, 4, 8, 6
      >
      > Add to these statement a look a MR1745569,
      > http://primes.utm.edu/references/refs.cgi?author=Suzuki
      > I have a scaned it if anyone wants a copy.
      >
      > Because of the above, 4*n+/-1 and 6*m+/-1 are the only ways to
      state
      > all primes factors with only two Dirichlet equations, and because
      > 4206 < 6!*6, I don't think there are any more possible. All other
      > numbers > 6!*6 have some way of having numbers > 36 = 6^2 in the
      P2
      > = p1*p2 product (prime factors are of 6*n +/- 0, 1, 2, 3, 4, or 5,
      n
      > < 6) + prime as to Chen's theorem (all even = P2 + p3).
      >
      > I do see how this can be used as part of the proof of the t-prime-
      GC
      > if anyone is up to it.
      >
      > Can anything more be said?
      >
      > John
      >
      >
      > --- In primenumbers@yahoogroups.com, Harvey Dubner <harvey@d...>
      > wrote:
      > > I had a paper published in Journal of Recreational Mathematics,
      > Vol.30(3),
      > > 1999-2000, entitled
      > > "Twin Prime Conjectures" which included the conjecture,
      > >
      > > Every even number greater than 4208 is the sum of two t-primes
      > where a
      > > t-prime is a prime which has a twin.
      > >
      > > This was verified up to 4.10^11 and included strong evidence
      that
      > the
      > > conjecture would hold for larger numbers. The paper also
      includes
      > > interestng comparative Goldbach data.
      > >
      > > I will be happy to send a pdf copy of the paper to anyone who
      asks.
      > >
      > > Harvey Dubner
      > >
      > > PS: No, the paper does not include a proof of the above
      > conjecture or GC.
      > > PPS: No, I am not working on such a proof.
      > >
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