I’m quite curious about Prime Numbers. Probably, most people reading this will know what Prime Numbers are. For those that don’t here’s a definition:
Prime numbers are positive integers greater than 1 that can only be divided by two positive integers – themselves and 1.
These are the prime numbers below 20: 2, 3, 5, 7, 11, 13, 17, 19.
1 isn’t regarded as a Prime Number because it doesn’t fully satisfy the definition. It is only divisible by one positive integer – itself. It hasn’t always NOT been regarded as a Prime though. There are three definitions historically speaking.
- The currently popular definition which excludes 1 and considers two to be the smallest Prime. A mathematician friend says this is mostly because it makes it easier to state certain proofs.
- A historical definition favoured by mathematicians in past centuries, which includes both 1 and 2 as Prime Numbers
- And then there are the ancient Greek mathematicians who insisted Prime Numbers were always odd numbers, so excluded 2, but also maintained that 3 was the smallest Prime Number.
There is no “biggest” prime, but they become less frequent as they get bigger. The record is currently held by 2^82,589,933 − 1 and has 24,862,048 digits. It was found by the Great Internet Mersenne Prime Search (GIMPS). They’re a collaborative project of volunteers founded in 1996 by George Woltman (pictured), a computer scientist from North Carolina, USA. His software PRIME95 is also used by gamers who need to stress test the stability of their systems when overclocking them.
Prime numbers are important for some encryption algorithms like public/private key encryption, RSA (Rivest-Shamir-Adleman) public key cryptography, Diffie-Hellman key exchange, and the Digital Signature Standard (DSS) cryptography schemes.
If you’re interested enough to explore this further, you can get a list of all the Prime Numbers up to 1000 billion here. There’s also a website called “Prime Curios” located here. This contains some interesting facts, stories and coincidences about Prime Numbers like: 3 is the smallest odd Fibonacci prime. It is the only Fibonacci prime with a composite index number: 3 = fib(4).
Another favourite from the Prime Curios site is the Pi Prime. This is a prime number embedded in the decimal expansion of π. More specifically the first six digits of Pi: 314159. Here are some interesting fact-lets about it:
- The squares and cubes of this prime, in reverse concatenation, are primes. [Silva]
- The six-digit combination to Ellie’s small office safe in the novel Contact by Carl Sagan.
- 314159 is a twin prime formed from three two-digit primes that are all members of twin prime pairs. [Silva]
- Vasilios Gardiakos points out in his “Document Alpha” that 314159 is an emirp. An emirp (prime spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. Here is the Wikipedia Page on Emerps.
Anyway, my interest in Prime Numbers has led me to examine my own interaction with these curious numbers and I’ve come up with this – my date of birth: March 12, 1956 – written in the British style is 12-3-56 – giving me the integers 1, 2, 3, 5 & 6. These are respectively,
- The divisor of primes
- The first prime number
- The first odd prime number
- The smallest balanced prime
- The smallest number which is a product of two distinct primes
So, you know when to send me a birthday card.
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