The cache is not at the posted coordinates.
This cache is part of the GAG6 event cache. Do not seek this cache until after 6:00 p.m. April 8, 2005.
Mathematicians and non-mathematicians have been fascinated for centuries by the properties and patterns of numbers. They have noticed that some numbers are equal to the sum of all of their factors (those whole numbers that divide evenly into it) not including the number itself. The smallest such example is 6, since 6 = 1 + 2 + 3. Such numbers are called perfect numbers. A positive integer is called a perfect number if it is equal to the sum of all of its positive factors, excluding itself.
The search for perfect numbers began in ancient times. The first three perfect numbers: 6, 28 and 496 were known to the ancient mathematicians since the time of Pythagoras (circa 500 BC).
Euclid (circa 300 BC), the famous Greek mathematician, devised a simple method for computing perfect numbers.
Begin with the number 1, and keep adding the powers of 2 (i.e. 1+2+4+8 etc), until you get a sum that is a prime number (a number that is only divisible by 1 and itself). A perfect number is then obtained by multiplying this sum by the last power of 2 that was added.
For example, 1+2=3 and 3 is prime. Therefore, 6 (3 multiplied by 2) is a perfect number. Similarly, 1+2+4=7 and 7 is prime. If we multiply 7 by 4 (the last power of 2) we get 28, which is a perfect number. 1+2+4+8=15, which is not a prime (it is divisible by 3 and 5). Therefore, 15 x 8 = 120 is not a perfect number.
We do not know how many perfect numbers there are. So far, there are 37 known "perfect" numbers. Obviously, this is not all of them. There are many that we will never know. We don't even know if the 37th number found is the 37th number; there may be another perfect number between the 35th and the 36th. It is very likely, too, that there are many more that we will NEVER know.
Nobody has found any odd perfect numbers, but we do not know if any odd ones exist. If any odd perfect numbers exist, they are not based on the above method of calculating perfect numbers.
To find this cache it is necessary to calculate or find the 5th perfect number. Replace the “000” in the posted north coordinate with the leftmost three digits of this number, and replace the “000” of the posted west coordinate with the rightmost 3 digits of this number.
The trail is easy (after the snow melts and it dries up) until the last few meters.
Have a perfect day.