PGA 22 Mystery Cache

Penrith Geo Art

A series of puzzles and wherigo caches in and around the Penrith area. These caches are of various sizes but as always when out caching bring your own pen.

The cache is not at the listed coordinates.

Prime Numbers

A prime number p is a natural (discrete) number that has exactly two positive divisors: one and itself. Examples of prime numbers are two, three, five, and seven. In Elements, Euclid proved that there are infinitely many prime numbers. If a number p is not prime (i.e., p can be written as the product of two other numbers each strictly between one and p) then p is called a ‘composite number’.

The prime numbers are multiplicative building blocks of the natural numbers, meaning that each natural number can be written uniquely as the product of finitely many prime numbers, a result known as the Fundamental Theorem of Arithmetic. The fact that every number (no matter how large it is) can be factorized into primes, or the fact that two very large prime numbers can be multiplied to give rise to another number, has implications for computer security since it is very difficult to figure out quickly how an extremely large number can be decomposed into two prime numbers. This aspect is used in the encryption of messages, where in order to undo the encryption and read the message, one needs to know the prime numbers used for encryption.

As well as their importance in Cryptography, prime numbers also appear in biology where, for example, some species of cicadas have life cycles of 13 years or 17 years, which gives them an evolutionary advantage.

Did you know?

• The only even prime number is two, all other even numbers can be divided by two.
• If the sum of a number’s digits is a multiple of three that number can be divided by three.
• No prime number greater than five ends in five, any number that ends in five can be divided by five.
• The luckiest and unluckiest numbers are prime
• Zero and One are not considered prime numbers.
• 73,939,133 is so far the only prime number that if you remove a digit from the right-hand side, it remains a prime number.
• The largest known prime number as of December 2020 is 2^82,589,933-1 a number which has 24,862,048 digits.

You can check out the wiki article here for more information and prime numbers and you can find yet more fun facts on prime numbers here.