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by Hugh Sasse

In the book "Starburst" by Frederik Pohl ISBN 0-345-27537-3, page 56, without
really spoiling the plot, some characters complain about the verbosity of
communications and encode a message by Gödelizing it (detailed on page 58).

The encoding works by taking each successive character of a message and raising
each successive prime to some function of that character, and multiplying these
powers of primes together. So for example we could use the ASCII code + 1 to
allow for nulls to be encoded. Then "Ruby\r\n" would end up as:

	(2 ** R) * (3 ** u) * (5 ** b)....
	
	10992805522291106558517740012022207329045811217010725353610920778
	28664749233402453985379760678149866991742205982820039955872246774
	86029159248495553882158351479922840433375701904296875000000000000
	00000000000000000000000000000000000000000000000000000000000000000
	000000

The idea is partly to obscure the message by the amount of factorization needed.
This quiz is to write a program to Gödelize a message, and a program to
deGödelize it.

The funtion used to map characters described in the book is "A" => 1, "B" => 2,
etc and an example is given where spaces are 0. Nothing further is said about
punctuation, or lower case. The message sent in the book is:

	msg = (3.875 * (12 ** 26)) +
	     (1973 ** 854) + (331 ** 852) +
	     (17 ** 2008) + (3 ** 9707) + (2 ** 88) - 78

which it turns out has lots of 0 powers in it, so I strictly don't need the
ASCII + 1 I've used in my example, I could use just ASCII, and the nulls would
not increase the size of the resulting number. This further means that if a list
of characters is sent in decreasing frequency order with the message, the most
frequent could be encoded as 0 and the number would be that much smaller. In
English it is likely to be an "e" or " " which ends up coded as 0.

Interesting things arising from this:

	1 Finding the power once a prime is selected
	2 Getting the list of primes in the first place
	3 encoding of characters, as mentioned above
	4 representing the number that results from encoding.