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## Prime Factorization

A cache by Cano
Hidden : 8/1/2008
In Maine, United States
Difficulty:
Terrain:

Size:  (small)

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### Geocache Description:

There is nothing on given coordinates. I took coordinates of cache N44°AB.CDE W68°FG.HIJ and multiplied numbers ABCDE*FGHIJ together and got number 2164816427. Your job is to figure out what numbers I used. Since both are prime numbers, there is only one solution. Larger one is latitude (N) and smaller one is longitude (W).

In number theory, the prime factors of a positive integer are the prime numbers that divide into that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicity. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization. Determining the prime factors of a number is an example of a problem frequently used to ensure cryptographic security in encryption systems; this problem is believed to require super-polynomial time in the number of digits- it is relatively easy to construct a problem that would take longer than the known age of the Universe to calculate on current computers using current algorithms. Don't worry, prime factorization of given number, won't take you so long ;-)

Cache is not winter friendly, you probably won't find it under snow and you may damage it if you step on it.

Pnpur vf uvqqra haqre ebbgf bs snyyra gerr.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)

### Inventory

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