## What are prime gaps and who is Yitang Zhang?

You have probably read a news about one professor proving The Prime Gap conjecture. In this post, I will give you an overview of what the excitement is all about in the mathematics community.

Prof. Yitan Zhang (courtesy of UNH via Slate.com)

This post is written for the high school students and those who are interested in mathematics that are non mathematics majors.

What are Prime Numbers?

Most of us are familiar with prime numbers. A prime number is a positive integer that is divisible only by 1 and itself.  The number 5 is a prime number, while 8 is not prime because 8 is divisible by 2 and 4. If we examine the 10 positive integers, it is easy to see that only four are prime numbers: 2, 3, 5 and 7. In the figure below, shown are the prime numbers less than 100. » Read more

## 4 Types of Composite Numbers You Probably Have Not Heard Of

There are numbers that are named because of their special characteristics. Prime numbers for example are unique because they only have two factors, 1 and itself.  Composite numbers, on the other hand, have more than two factors.

Speaking of composite numbers, there are different types of such numbers that you probably have not heard of. In this post, we familiarize ourselves with these types of numbers. » Read more

## Mersenne Primes Under the Microscope

What are Mersenne Primes?

The recent discovery of the largest known prime number which is 17 million digits highlighted the importance of Mersenne primes.  This newest prime number and the thirteen largest primes are all Mersenne primes. But what are Mersenne primes really and why are they important in finding the largest prime numbers?

If a prime number can be expressed in the form $2^n - 1$, $n$ an integer, then it is said to be a Mersenne prime. The name came from Marin Mersenne who studied them, a French monk and well-known mathematician in the 17th century.

Many early mathematicians saw and conjectured that if n is a prime number, $2^n - 1$ is prime.  For instance, in the figure above, for $n = 2, 3, 5, 7$ which are prime numbers, their corresponding $2^n - 1$ values are also prime numbers. However, this is not true in general since $2^{11} - 1 = 2047 = (23)(89)$ is not prime.  » Read more

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