It's A Prime Cache! Mystery Cache

It's A Prime Cache!

Prime numbers. Perhaps you remember them from school. If not let me refresh your memory. Prime numbers have long fascinated amateur and professional mathematicians. An integer greater than one is called a prime number if its only divisors are one and itself. The first prime numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible by 2 and 5.

There is a special category of prime numbers called Mersenne primes. A Mersenne prime has the form 2^P-1, where P is also a prime number. The first few Mersenne primes are 3, 7, 31, 127, etc. How many Mersenne primes are known to exist? The answer to that question shall be "A".

The largest known Mersenne prime has 9,808,358 digits! Billions have 9 digits. Trillions have 12 digits. Quadrillions have 15 digits. Quintillions have 18 digits. To be honest I don't know what comes after that. To give you an idea of just how big this number is, some estimates have it that our entire universe contains 10⁸¹ atoms. That's an 82-digit number. In the entire universe! Boggles the mind, doesn't it?

What is the prime exponent that yields the largest known Mersenne prime? The answer to this question shall be known as "B".

Amazed? Entertained? Ready to find the cache? Good! Here's how:

To obtain the latitude, multiply "A" by 7 then subtract 10. Divide the result by 1000 and add it to the posted minutes of latitude above. The second, third, and fourth digits of "B" comprise a three-digit number, "C". To obtain the longitude, subtract the three digits to the right of the decimal minutes of longitude above from "C" and multiply by 10. Now substitute the result for the minutes to the right of the decimal above (If you get fewer than three digits you'll need to insert leading 0s).

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