"God created the integers, all the rest is the work of man". The 18th-century mathematician Leopold Kronecker believed that all arithmetic should be underpinned by the "natural numbers" (1, 2, 3, 4, etc).
In contrast, modern mathematics is rich and diverse, and recognises negative numbers, fractions, irrational numbers, and imaginary numbers (and even more abstract concepts) as equally valid as the natural numbers. However, there's still a branch of mathematics that concentrates on the integers. This is Number Theory, and is a surprisingly complex field in its own right. For example, Fermat's Last Theorem is a Number Theory problem, but it took 357 years to prove, and required the creation of whole new concepts and techniques to finally prove.
Number Theory is also concerned with the prime numbers, which are natural numbers that can only be divided by one and the prime number itself. Prime numbers are sometimes considered the building blocks of all other numbers, as every natural number is a unique product of one or more primes.
It can be shown that there are infinitely many primes, although their frequency of occurrence becomes progressively smaller as the numbers become larger. Various efforts are ongoing to use networked computers to find ever larger prime numbers, such as the Great Internet Mersenne Prime Search (GIMPS). This project has found the largest prime number so far, with a massive 12,978,189 digits.
Prime numbers aren't just a scientific curiosity either – they are fundamental to many of the cryptographic systems which keep Internet transactions confidential.
Anyway, here's what you're really after – how to find the cache. First place the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 into the grid below, according to the following rules:
- Each digit appears only once.
- The 4 digit number B is a multiple of the 4 digit number A.
- Of the five 2 digit vertical numbers, four of them are prime.
- No 2 digit or 4 digit number starts with a 0.
Then the cache can then be found at S 34° 55.vwx E 138° 36.vyz
You'll need to time your visit carefully, or use extreme stealth when accessing the cache. When replacing, please try and push the container to the back of its hiding spot. Good hunting!
