about prime numbers

Each new prime is an extension of the bounds of human mathematical knowledge

Yesterday I read a news about scientists found out the largest prime number known. It starts with a 4, ‘continues on for’ 23 million digits, then ends with a 1.

What is the prime number

A prime number can only be divided evenly by itself and by the number 1. The number 2 is prime because it can only be divided by 1 or 2 to give a whole number. Other example of prime numbers are 3,5,7,11,13,17 and 19.

Prime numbers are essential to modern life. They are used in everything from securely encrypting banking information to the random number generators used for visual effects in the latest movies.

Discovering Prime Numbers

About 2300 years ago, the Greek mathematician Euclid wrote a book called “The Elements”. He showed that prime numbers did not just stop at a certain value, there are infinitely many of them.

About 100 years later, another Greek mathematician Eratosthenes came up with a way of finding prime number. His method was called the Sieve of Eratosthenes. A sieve is a tool that drains water. Eratosthenes’ mathematical drains away non-prime numbers from prime numbers.

Here is how it works:

• Write down all the numbers from 1 to 100.
• Cross out 1, since it’s not a prime number. A prime number can be divided by exactly two numbers. The number 1 can only be divided by 1.
• Circle 2, the smallest prime number, then cross out every multiple of two. These are the numbers 4,6,8 etc. In other words, cross out every second number.
• Circle 3, the next prime number. Then cross out all the multiple of 3, which are 6,9,12,15 etc. Some have already been crossed out.
• Circle the next number not circled or crossed out, which is 5, then cross out the multiples of 5, which are 10,15,20,25 etc. Some have already been crossed out.
• Continue doing this until all the numbers have been circled or crossed out. The circled numbers are the prime numbers from 1 to 100.

Christian Goldbach was a historian and mathematician. He made another discovery about prime numbers in the 1600s. He said that

every even number could be weitten by adding two prime numbers together.

For example, 20 can be written as 17+3.

Even today, we are still not sure if Goldbach’s idea is true. But scientists do know that it’s true for every even number between 2 and 400,000,000,000,000.

An example In Nature

Cicadas are plant-eating insects. They spend almost all their lives underground before coming out as adults. For some kinds of cicada, this happens after 13 or 17 years.

Note that 13 and 17 are prime numbers. Scientists who have studied these cicadas think there’s a reason for this. Both predators and prey have certain life cycles, which determine how long it takes for those animals to reach a peak in their numbers. The reserchers found the best times for the cicadas to emerge from the ground were in life cycles that were prime numbers, like 13 and 17 years, so a predator’s life cycle also has to be 1, 13 or 17 years. The odds of being prey happening are much lower.

A Million Digits Longer Than The Previous Prime

The newest prime number is generated by multiplying 2 by itself 77,232,917 times, then subtracting 1. The way this is calculated makes it a Mersenne Prime. Named after the French theologian and mathematician Marin Mersenne, these types of primes are always calculated as a power of 2 minus 1. The number - which can be written in shorthand as M77232917 - is nearly 1 million digits longer than the last confirmed prime discovered in 2016.

When M77232917 is written out as all 23,249,425 digits, the number contains every digit from zero through 9 roughly 2.3 million times each. Like all prime numbers, it appears to be random. Some researchers suggest, however, that faint patterns shape the distribution of prime numbers. These faint patterns are enough to help narrow the search for new prime numbers. This helps researchers predict how many primes will exist within a range of numbers.

Determining if a number is a prime is simple in theory, all you need to do is divide it by all primes smaller than itself. If no other primes can divide it evenly, it must be a new prime number. In practice, however, this approach is time-consuming for a extremely large numbers, even with modern computers capable of precise and quick calculations. Instead, algorithms take advantage of a number theory trick called the Lucas-Lehmer test that only works for Mersenne primes to speed up the process.

Welcome to the list of primes, M77232917, and enjoy your time as the largest prime number while you can. One thing is certain: One day, a new largest prime number will be discovered.