Puzzle Solvers Toolkit #2 Mystery Cache

The cache is not at the posted coordinates but is less than 2 miles away

This puzzle is the second in a series to highlight a tool that should be in every puzzle solvers toolkit.

Although some puzzles require you to find the factors of a number, it’s been my personal experience that many puzzles are looking for the Prime factors of a number. Prime factors, as the name implies, are the Prime Numbers (2, 3, 5, 7, 11, ...) that are multiplied together to obtain the number. For example, the Prime factors of 12 are 2 x 2 x 3 which is typically written in exponential form as 2² x 3¹. There are many Prime factor calculators online including this one.

Most online Prime factor calculators work great for a small number but what if it’s a really LARGE number? I’m glad that you asked .

My favorite tool for Prime Factorization of large numbers is Factoris. You can also use Wolfram Alpha to calculate Prime factors but Factoris advertises “There is no limit on the values (but the execution time is limited to about 20 seconds).” This should be more than enough for a geocache puzzle.

Now let’s explore a couple of ways to hide coordinates by using Prime factors. Don't forget that a number raised to the power of 1 is the number itself. For example, 17=17¹.

Find the latitude of the cache by determining the Prime factors of these numbers:

2187 32 61

Find the longitude of the cache by determining the Prime factors of this number:

1980788956314532887623709023450551755914

Now go find the cache.

There is room for small trade and signature items. Don't forget to bring your pen.

Enjoy!

You can validate your puzzle solution with Certitude.

Thanks to teamajk (NY) for the beta-test.

Congratulations to lmt000 on FTS and FTF.