The Largest Known Prime Number

Quick!  How many prime numbers can you recite, starting at 2 (1 is not prime!)?  Let's see... 2, 3, 5, 7, 11, 13, 17, 19, 23... the further you go, the more you have to think about it, right?  What you have to consider is whether each number you evaluate is only divisible by itself and 1, or if it can be divided by other numbers.  If it's only 1 and itself, you've found a prime number!  But as you count up higher, there is a higher likelihood that these bigger numbers are going to have some out-of-the-ordinary factors that you don't automatically think about.  So then, you can see the role that computers play in finding prime numbers.

Computers can do all of the hard calculations.  They can check to see for any given number if another number can completely divide into it.  This may seem simple if you consider a number like 35 (which isn't prime, because there is 1x35 and also 5x7), but what about considering a number like 64,092,283? It's not likely that you are going to check to see if it has any factors in a short amount of time, but a computer can do it relatively quickly.  Of course, the larger the number, the more calculations it has to check and so even they will take some time.

When you get up to the REALLY large numbers, you have to consider that the computer needs lots of time to evaluate all possible factors for each number.  Since prime numbers become more rare as you count higher, a larger portion of the values that the computer has to spend time evaluating will actually work out to be non-primes.  For this reason, the most recent prime number was discovered FOUR YEARS after the previous prime was reported.

There is currently a distributing computing project named GIMPS (Great Internet Mersenne Prime Search) that is actively doing calculations and checks to find the next prime number.  Curtis Cooper from the University of Central Missouri was the one who reportedly found this latest prime, and it is easy to see why it has taken so long to find.  This largest prime number ever found has more than 17 MILLION digits.  It is the number represented by 2 ^57,885,161 -1.  Now, imagine having to check that number by hand to see if it had any other factors to rule it out as a prime.  This may not be the most glamorous job for a computer to do, certainly not as entertaining or visually appealing as editing digital photographs or playing video games, but it definitely is a job meant for a computer.

On that note, Phillip Bump got creative with this 17 million digit monster.  He divided it into 6 digit chunks, each chunk then representing an RGB colour, and then plotted out the resulting colour distribution.  From that point of view, the following picture is essentially the fingerprint of this prime.  Maybe working with primes IS a visual art!

The Largest Known Prime Number - by Phillip Bump

Free Online Courses with Credits - Update

In one of my recently published posts here on my site, I discussed some options available for people looking to find free online courses with certificates.  Massive open online courses (MOOCs) have had an increasing role in education discussions over the last couple of years, and world-class institutions such as Harvard and Stanford now offer their own versions of distance learning degrees.  In very coincidental timing, I came across an article since I put up that post that further promotes MOOC online classes.

In a move that may go a long ways towards giving online degree courses more recognition and respect, the California State University system has announced a partnership with Udacity, a startup company that produces online college classes, to begin offering a series of introductory courses FOR CREDITS.  Subjects offered will include remedial algebra, college level algebra, and introductory statistics.  For the time being, these courses are being offered to a limited number of students, for the price of $150, which is many times cheaper than a more typical college or university tuition.  These MOOC online classes will involve watching videos and participating in online interactive exercises and quizzes.  Students will also have access to online assistance from professors or other mentors.

In a similarly high profile news update, Coursera (arguably the most popular and familiar platform for offering free online education) has announced that it has received approval to make five of its courses available for college transfer credits, including mathematically oriented subjects such as pre-calculus, single variable calculus, and intermediate algebra.  Naturally, this can be viewed as an experiment before potentially increasing the number of its courses that would qualify for this credit equivalency.

These massive online courses are gradually becoming more popular and important in schools' education programs and policies, as can be seen by the increasing number of schools that have begun offering variations of these correspondence courses and the availability of transferrable credits towards a degree.  One of the main problems, however, is the alarmingly high dropout rate.  Some of these MOOC online degree courses have 90% dropouts.  That may be because of a high number of people who sign up to just browse the course without ever having an intention of seeing it through to completion, or some may find that there is not enough support or assistance offered, something that regular attendees of campus institutions take for granted.  As such, this new program by Udacity will include many mentors available to assist and other student support services, such as check-ins and email encouragements - simple but effective touches to keeping students interested and motivated.

While these programs should probably best be viewed as pilot programs with uncertain futures, if they are received well it should be expected that they will increase their course offerings that carry transfer credits.  This will go a long ways to proving the value of the MOOC concept, and will likely cause a cascade of educational institutions to begin offering their own variations of the platforms.  It feels as though we may be at a pivotal point in education history.  Learning has traditionally been done in schools with lectures, hands-on experience, and supervision - all at high cost - while online education programs - especially the free ones - have typically been regarded as supplementary to these customs.  However, with some of these platforms gaining credit equivalency, these may be some of the first steps for these services towards gaining recognition for providing meaningful education that is widely available and affordable - a real education revolution.

Sheldon Cooper's Clock and Equation Watch

This one is for all the hardcore math nerds out there.  No normal person is going to have these in their life!  I have seen these several times over the last few days, and thought that my math blog would be the perfect place to repost them!

As anyone who watches The Big Bang Theory knows, Dr. Sheldon Cooper is a theoretical physics genius.  Therefore, it would almost be expected that if you were to visit his home or office, you would find a brilliant timepiece such as this on the wall:

Dr. Sheldon Cooper's Clock

Sheldon Cooper's clock can only be used by true mathematical students!  If any regular person were to try to tell the time by looking at this clock, they would be completely lost and would have no idea what time it was!  Well, maybe that's going a little far.  It would certainly be an interesting exercise for math students to explain why each equation is equal to the known numbers on a regular clock face.

Of course, even crazy smart math professors and scientists need to leave their home and office once in a while.  For those rare events, I'm sure they would be more likely to leave their keys or iPhone at home rather than forget to wear one of these staggeringly beautiful equation watches!

Equation Watch

I don't think these clocks need any more explanation.  They are both brilliant and nerdy to a nearly unimaginable degree, and that's more than enough reason for me to share them here on my site.  :)  I don't want to claim ownership of either of these images, but I'm not sure who to accurately attribute them to, unfortunately.  Well done, though.

Top 5 Most Popular Posts of January 2013

As a new feature I am adding to my site, at the end of every month I am going to review my traffic data and then present my most popular posts.  In case anyone misses the posts on their original publications dates and then falls behind on my blog, this will now give them another chance to see the articles that the most readers are talking about.  So, without further ado, here are my top 5 most popular posts for the month of January 2013.

1. 20+ Free Math Worksheet Sites for Teachers.  A great resource that contains links to several different websites that offer high quality math worksheets for free.  You can print these practice sheets and use them in class or at home to study.  These are all high quality sites, and I recommend checking them out for your worksheet needs.


2. How to use LaTex Equation Editor.  If you have any reason to type math equations on your computer, you are likely familiar with the difficulties in getting your formulas to look anything like what you would write on paper.  However, if you use the LaTex Equation Editor, you can get your onscreen and online math equations to look exactly like you want.  Textbook perfect.


3. Japanese Multiplication Method.  To learn about an alternative method of multiplication popular in the Japanese culture, take a look at this post.  It's a different perspective on a very common mathematical technique that is both functional and entertaining.


4. Trigonometry - The Sine Function and SOHCAHTOA Explained.  One of my oldest posts, and still one of my most popular.  This post explains the concept of the sine function in trigonometry, and how it relates the to memorization trick most students know as SOHCAHTOA.


5. Free Online Courses with Certificates.  This is one of my most recent posts, and it has gotten a lot of traffic.  It discusses several options that are available to anyone interested in taking online math courses, some of which actually will grant you certificates or transferable university credits.  Online education is a rapidly expanding offering, and those institutions and services listed in this post are among the most popular.

To find more great explanations and discussions of math concepts on my site, browse the Math Concepts Explained table of contents.  Alternately, you can enter your topic of interest in the search bar at the top of every page.

If you enjoy Math Concepts Explained, I invite you to join the many other students, teachers, and math enthusiasts who follow my site:

• Like my page on Facebook.
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Thanks to all of my visitors for your support!

Free Online Courses with Certificates

Instead of presenting a math concept in this post, I would like to provide a bit of information for those interested in free online courses with certificates.  Many of the visitors I get to this site are students currently enrolled in their traditional school math programs, and they simply need help understanding their homework or a particular new topic they learned.  Other visitors may be more of the 'math enthusiast' variety, and are just reading these posts because they simply love everything to do with mathematics.  However, there may be visitors who don't have the luxury of actually attending a school to pursue their education.  Maybe there isn't a school nearby, or a good math program isn't available, or maybe they left school early and are trying to complete their education later in life.  For these people, one option available to them is online math courses.  In this post, I thought it might be helpful to present some options to consider, and I will mention what these programs have to offer.

Keep in mind that I am not affiliated with any of these, nor do I have any actual experience with them.  I am just going to present some compiled information for you to consider if you are interested.

In my research, one site that consistently came up in the search results was Open Culture, who market themselves as "the best free cultural and educational media on the web."  On their site, they have a list that contains 200 free online courses (which are "massive open online courses", or MOOCs) offered by various universities and institutions, some of which will issue a certificate of completion when you get through the course.  Some instead will provide you a statement of accomplishment.  These are good and worthy achievements, though they typically don't equate to transferable university credits.  You can find things on this list such as Introduction to Astronomy, or Introduction to Finance... topics which are mathematical in nature.  There are also classes offered with no certificates available, but may be more specific to mathematics, such as Introduction to Statistics.  It appears that this list gets updated frequently, as the courses are listed monthly as they are available, but there are also courses available that have no fixed start date, and so you can sign up and begin whenever you want.  I can't fairly comment about the quality of the material offered, but a brief look at some of the outlines available suggests that if you are serious about taking online math courses (or other subjects), these will teach you something.

Perhaps a more famous name than the previous site is the Massachusetts Institute of Technology (MIT), one of the more prestigious schools in America that you can attend.  A few years ago, they announced the beginning of a new educational venture: MITx.  While students that physically attend MIT (and gain the honour of being on campus, doing amazing things, and meeting brilliant professors), MITx promises to offer a similar quality of education online and for free.  And even better, they have said that they would issue a certificate to show that you have mastered the subjects offered, though it appears that obtaining these credentials will cost a nominal fee.  A quick glance at their site reveals a variety of topics available.  Several other schools and sites have applauded MIT for this initiative, so hopefully other institutions will follow their lead and we will have more high-quality schools offering free, recognized education.

Some reports actually suggest that the concept of MOOCs is the beginning of something big in education.  Another very well known school participating in this trend is Stanford University.  They offer several courses to take online, with varying start dates and topics.  A quick glance at the list of classes available online reveals several that are mathematical in nature, though most may be considered to be more advanced math concepts, such as algorithms and databases.  Nonetheless, for a free course that will teach you something, you won't find a much more reputable name than Stanford University, so this list of courses is definitely worth keeping an eye on, especially as it appears to be updated periodically.

Beyond these famous educational institutions, there are a few more sites that I will mention here that are extremely popular with people looking for an online education.  Coursera is a site that has partnered with top universities from around the world to offer free online courses to anyone who wishes to take them.  High quality video lessons and interactive exercises, combined with a global community of like-minded students, help make this service incredibly attractive and useful.  When I checked, there were 33 universities participating in the Coursera program, with a wide range of topics from music to medicine.  Of course, mathematics is a dedicated section with many options available from which to choose.  Algebra, calculus, and more advanced math concepts are available.  Looking at the breadth of material available, it is easy to see why this service is so popular!

Similar to Coursera, Class Central is a MOOC aggregator.  It appears to tap into the available course lists of many top universities, and makes them accessibly in an easily searchable database.  You can quickly see if there are any online courses available for your selected topic with a simple search right from their home page.  Class Central doesn't appear to offer any courses themselves, so anything you find there will be found offered by the originating institutions.  I only include it here because it seems like it could be useful to you in your research on choosing an online course.

Finally, though it's the same as the online courses I've mentioned above, Khan Academy is a very popular and useful site that provides many video lessons on several topics across a wide variety of subjects.  For example, in the math section, there are all sorts of videos that describe particular concepts, with very good explanations and examples.  If you are looking for a quick lesson on a topic, and you aren't interested in going through a whole course to obtain credits or certificates, Khan Academy should be one of the first places you look.

Of course, if you are looking for help on math concepts, you can always search my site or contact me to see if you can find the assistance that you need.  As I said, I have no experience with any of these services that I've discussed on this page.  I have only done a basic research and compilation to bring this information together in one place for you to consider if you would like to further your education by taking free online courses.