GIMPS Discovers The Largest Known Prime Number Yet

The Great Internet Mersenne Prime Search (GIMPS) discovered the largest prime number yet on January 7, 2016. The number is 2^{74, 207, 281} - 1. It contains 22,338,618 digits. If you are wondering how long it is, suppose that you can write an average of 2 digits per second, you will be able to finish writing this number in about 129 days without eating, sleeping, or toilet break. Using the same rate, if you are going to write this number for 6 hours a day, then you will finish it in about 517 days (roughly one and a half years).

GIMPS has been calculating large prime numbers since 1996 and has discovered 15 of the largest known prime numbers. As of this writing, the 11 largest prime numbers are Mersenne primes. Mersenne primes are prime numbers of the form 2^n - 1 for some integer n. Three of the smallest Mersenne primes are 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31 .

Question: Are all positive integers of the form 2^n - 1 prime numbers?

For the non-math persons, prime numbers are positive integers that can only be divided by 1 and itself. For example, 5 is a prime number since you cannot divide 5 by any number except one and itself. On the other hand, 8 is not a prime number because 8 can be divided by 1, 2, 4, and 8.

It was already proven by Euclid (some 2300 years ago) that there is no largest prime number, so the search for large prime numbers will never end.

Some of the most useful application of prime numbers is cryptography, particularly internet security. It’s what makes your password safe. It is what makes shopping safe. Well, you still have to be careful though.

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

The Amazing Mathematics Illuminated

Mathematics Illuminated is an amazing multimedia resource created by Annenberg Media. It contains text articles, videos, and java applets that discusses mathematics ranging from the most ancient to the most modern. The title of 13 chapters are the following.

  1. The Primes
  2. Combinatorics Counts
  3. How Big is Infinity
  4. Topology’s Twists and Turns
  5. Other Dimensions
  6. The Beauty of Symmetry
  7. Making Sense of Randomness
  8. Geometries Beyond Euclid
  9. Game Theory
  10. Harmonious Math
  11. Connecting with Networks
  12. In Sync
  13. The Concepts of Chaos

It also contains textbooks, facilitator’s guides, participant’s guides, interactive applets and many other teaching tools that can be used in teaching and learning mathematics.

If you are a mathematics teacher or enthusiast, Mathematics Illuminated is really worth visiting.

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