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A Easy New Years Prime Puzzle

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  • Milton Brown
    The following 70 digit PRP is a message encoded with the attached trap-door function, please decode: 39099 93338 35338 35310 54172 52911 36295 83331 05417
    Message 1 of 3 , Dec 31, 2005
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      The following 70 digit PRP is a message encoded with
      the attached trap-door function, please decode:

      39099 93338 35338 35310 54172 52911 36295
      83331 05417 13629 99333 63120 06010 10109


      Milton L. Brown


      1 9933 -12587
      2 7341 -96191
      3 63091 -9489
      4 28333 -11337
      5 13629 -9959

      6 4659 -7329
      7 9001 -22743
      8 3909 -2919
      9 48521 -3789
      10 59689 -28787

      11 55971 -44291
      12 170781 -1977
      13 29247 -4383
      14 25291 -45323
      15 116961 -17949

      16 38353 -3101
      17 26371 -4743
      18 3631 -3437
      19 20007 -41009
      20 55447 -237

      21 3663 -6063
      22 52793 -6569
      23 58333 -31781
      24 15679 -20177
      25 105417 -7067

      26 12379 -32991

      [Non-text portions of this message have been removed]
    • Phil Carmody
      From: Milton Brown ... Hmm, the following ain t much of a function , but let s see what we can extract... Lets look at the two
      Message 2 of 3 , Jan 1, 2006
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        From: "Milton Brown" <miltbrown@...>
        > The following 70 digit PRP is a message encoded with
        > the attached trap-door function, please decode:
        >
        > 39099 93338 35338 35310 54172 52911 36295
        > 83331 05417 13629 99333 63120 06010 10109

        Hmm, the following ain't much of a "function", but let's see what we can
        extract...

        Lets look at the two values as offsets of pairs of primes around 10^n for some
        n, and see if n helps define a simple substitution cypher, by mapping the
        values onto the range 1-26.

        > 1 9933 -12587 10^7
        > 2 7341 -96191 24
        > 3 63091 -9489 8 or 25 (how weird is that?)
        > 4 28333 -11337 3
        > 5 13629 -9959 4
        >
        > 6 4659 -7329 5
        > 7 9001 -22743 none in a sensible range - is this a 'space'?
        > 8 3909 -2919 6 or 9 (not so weird is seems)
        > 9 48521 -3789 none in a sensible range. Are these just unused codes?
        > 10 59689 -28787 32 (oh dear, 3 "out of range" values.)
        >
        > 11 55971 -44291 none in a sensible range
        > 12 170781 -1977 10
        > 13 29247 -4383 none in a suitable range

        The hit rate's not very high, so let's change tack, and look at the
        message itself:

        In base-26 it's
        01 21 03 21 12 01 14 10 06 13 08 14 14 09 09 14 00 22 20 03 15 00 24\
        25 23 19 10 16 18 11 06 11 08 14 06 24 17 14 02 24 25 01 10 14 16 12\
        01 15 12 01

        The sequence '14 14 09 09 14', if it were to occur in a single word, could
        narrow down the possibilities greatly. Unfortunately, my dictionary only
        contains the following that have that pattern:
        addressees
        fricassees
        greenness
        keenness
        lessees
        None of which seem particularly likely.



        By mapping 0->A, 25->Z to keep everything simpler, we get
        B V D V M B O K G N I O O J J O A W U D P A Y\
        Z X T K Q S L G L I O G Y R O C Y Z B K O Q M\
        B P M B

        Which has a distribution as follows:
        2 A
        5 B
        1 C
        2 D
        3 G
        2 I
        2 J
        3 K
        2 L
        3 M
        1 N
        7 O
        2 P
        2 Q
        1 R
        1 S
        1 T
        1 U
        2 V
        1 W
        1 X
        3 Y
        2 Z

        This is a bit too flat for a typical English language message, unless it's
        particularly contrived.


        OK, I'm stumped.

        Phil

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      • makeanote
        ... Milton, this puzzle was a little frustrating in its simplicity, but thanks for the well wishes. HAPPY NEW YEAR 2006 01 01 I m assuming (but could be
        Message 3 of 3 , Jan 2, 2006
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          > From: "Milton Brown" <miltbrown@e...>
          > > The following 70 digit PRP is a message encoded with
          > > the attached trap-door function, please decode:
          > >
          > > 39099 93338 35338 35310 54172 52911 36295
          > > 83331 05417 13629 99333 63120 06010 10109
          >
          Milton, this puzzle was a little 'frustrating' in its simplicity, but
          thanks for the well wishes.

          HAPPY NEW YEAR 2006 01 01

          I'm assuming (but could be wrong of course) that the final digits
          0109 were to generate a number that was PRP?

          To the group:
          The 'trapdoor function' contained firstly the letter of the alphabet
          1 9933 -12587
          (in sequential order A=1), then the next number was the corresponding
          pattern in the PRP. I didn't bother to work out the third number as
          the answer I was expecting was being generated anyhow.

          So, in the PRP beginning 3909 this corresponded to the letter H (8)
          and so on.

          Ian.
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