## A Easy New Years Prime Puzzle

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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
Message 1 of 3 , Dec 31, 2005
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]
• 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
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:
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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[stolen with permission from Daniel B. Cristofani]

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• ... 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
> 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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