NOTE: The listed coordinates are not the actual coordinates of the cache (they're an excellent place to park, though). To get the coordinates for the cache, you must solve the problem described below.
In the world of cryptography (codes and ciphers) a 'trapdoor' function is one which is easy to compute but difficult to invert. The classic example is multiplication of two prime numbers - pretty easy to compute. To run the computation backwards, you start with the product and find the two numbers you multiplied by finding the factors of the product. To find this cache, you'll have to find out just how hard factoring really is.
This cache is hidden on some prime real estate - mathematically speaking. The latitude (expressed as Nxx° xx.xxx") and the longitude (expressed as Wxxx° xx.xxx") have had the non-digits stripped out, yielding a 7 digit number for the latitude and an eight digit number for the longitude. Both of these numbers are prime. When you multiply the two numbers together, you get 57877010199083. If you factor that number, you'll get two prime factors (besides 1 and itself). The seven digit factor gives you the latitude, the eight digit one gives you the longitude.
The cache itself is a .30 caliber ammo can.
To reach the cache, you'll need to leave the trail, but no real bushwhacking is required. Parking at N47° 42.136" W122° 05.337"
1/26/07 The previous hiding location is now rather exposed with evidence of high water. Rather than risk a re-hide, I placed a new ammo can on higher ground to the southwest. Standing at your solved coordinates look to the southwest and you will see a log retaining wall, a bench and a large tree that are lie along the same bearing. Continuing along this same bearing another 15 to 20 feet will bring you to the new hide location which is about 100 feet from the puzzle solution.
(Current CO lashru, adopted from jcacher15).
Aug 2023: Replaced ammo can, camouflaged, and added certitude. Enter the exact coordinates from the puzzle solution. Offset detail for final in certitude. Please, please rehide well.
You can validate your puzzle solution with
certitude.