prime number

Properties of 2011

The number “2011” abounds with fun numerical and “visual-numerical” properties. Early into the new year, we experienced the time “1:11:11 on 1/1/11”. And this week, we had the even more auspicious “1:11:11 on 1/11/11”, at least with the date-writing convention we use in the United States. This week all the dates have been palindromes using the two-digit year convention, e.g., today is “1 14 11”, and if one uses the full four-digit year, this past Monday was “1 10 2011”, also a palindrome.

While text-based properties are fun, they are somewhat arbitrary and less interesting than mathematical properties of numbers. First, 2011 is a prime number, the first prime year since 2003. And from @mathematicsprof on twitter, we have this interesting coincidence:

“2011 is also the sum of 11 CONSECUTIVE prime numbers:
2011=157+163+167+173+179+181+191+193+197+199+211”.

In other words, this is not just a series of prime numbers, but all the prime numbers between 157 and 211. I like that the last prime in the series happens to be 211!

The Republic of Math blog follows the consecutive-prime inquiry further, with the observation that 2011 can also be written as the sum of three consecutive primes “661 673 and 677”.

From The Power of Proofs, we have the property that 2011 is the sum of three squares:

2011 = 392 + 172 + 72

However, any number not congruent to 7 modulo 8 will have such a property. I.e., if you divide 2011 by 8, you have 3 left over. So really 7 out of 8 integers can be expressed this way. Finding the series of squares can take some time, though.

Please feel free to share any other mathematical or fun coincidental properties in the comments below.

Carnival of Mathematics #35

We at CatSynth are delighted to be hosting the 35th Carnival of Mathematics.

The date “Friday the 13th” of course evokes many superstitions. And perhaps that is why we have so few entries so far this weekend. That having been said, we at CatSynth take a dim view of superstitions. Many of the traditions that led to the irrational fear of the number 13 (including skipping over of 13 in building floor numbers, etc) are the same ones that promote the unfair treatment of black cats. Neither has a place in a modern, rational, society.

Consider that 13th of the month is no more likely to fall on a Friday than any other day of the week. Over a period of 28 years, that is 48 “Fridays the 13th,” as described here.

Let us turn away from superstition and myth, so some of the more mathematical properties of the number 13. It is a prime number (indeed, the sixth smallest prime). It is also a well-known twin prime, and it is one of only three known Wilson primes. For those less interested that I am in prime numbers, it is also a Fibnoacci number, and the number of Archimedean solids.

You can find more about the mathematics and mythology of 13 at “13 the Unlucky”.

Last week’s host, the blog 360, has a post about 13 and other “unlucky” numbers. But they also contribute a demonstration, using Godzilla, of how to calculate the speed of a
dinosaur by its footprints.

Recursivity introduces us to the Open Problem Garden, a site collecting open problems in mathematics and theoretical computer science. He presents an open problem about discrete iterations that is easy to state yet frustratingly hard to solve, as are many of the great problems of mathematics.

Looking for a more modest challenge? Math and Logic Play presents a bicycle-racing puzzle. Practice your math skills while staying healthy and reducing your carbon footprint…

Larry Ferlazzo describes a site for math games and education in Tutpup Math & Spelling Games.

Andrée from meeyauw treats us to Sierpinski cookies and earings this week. Those cookies look pretty good, but challenging to make. Fractals are by nature very detail oriented, and I am by nature very not detail oriented. But I’m sure they would taste great in either case.

The state of math education (in the United States) in a frequent topic on Carnival of Mathematics. This week, female math professor critiques an elementary school math program at Life on the Tenure-Track. It seems that at least in some classes, teachers aren’t able to make it through the full syllabus.

More topics in math education can be found at Teach College Math, where we are introduced to the Math Girl videos. “Who says there’s nothing good on YouTube?”

For the more discriminating reader, we have Discriminating Determinants, third in a series from Matt-a-matical Thinking.

We get back to our theme of the number 13. The fashionablemathematician presents the sum of prime factors. For a prime number like 13, the sum is of course the same: 13. But are there other numbers whose prime factors sum to 13? Well, the number 22 has prime factors 2 and 11, which add up to 13.

Sometimes a mathematician can end up being an astrophysicist, especially on Friday the 13th, as is the case with this article from Math Trek.

That is all the posts we currently have. We will continue to add sites throughout the weekend, so please leave a comment or contact us if you would like to participate.



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The CatSynth Eighty-three

It seems like everyone these days has a “top 100 list”, indeed we are listed on a few of them. Well, we at CatSynth like to be different, so we're introducing the “CatSynth 83.” All sites related to cats, synthesizers, electronic music, or any of the other topics frequently discussed on this site like highways, mathematics, software, etc., can apply. We will list to top 83 participating sites. So come and join the only top-sites list based on a neglected prime number.