## 19 Jul Carnival of Mathematics #124

I am very pleased to be the hosting the 124th edition of the Carnival of Mathematics, organised every month by the awesome people at The Aperiodical. Following tradition, I would try to say something interesting about the number 124.

The usual properties of **124** are that it is composite and even. 124 is the sum of eight consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29). It is a nontotient since there is no integer with 124 coprimes below it, it is an untouchable number since there is no integer whose proper divisors add up to 124. The number n is *deficient* if the sum of all its positive divisors except itself is less than n, and 124 is such a number.The number n is *odious* if it has an odd number of 1’s in its binary expansion and 124 is an odious number.

Now, for some more interesting properties of the number. It is a repunit in base 5, that is in base 5 the number is written as 444 which is just a repetition of the same digit more than once with no other digits. 124 is the smallest number with the property that its first 3 multiples contain the digit 2.

Without further ado, let me list the submissions that we recieved:

- John Cook has written about the mystery curve and has provided links to many related posts.
- Wired has a nice article about internet art which is inspired by mathematics.
- In a similar vein, here is another one about art and mathematics.
- A very interesting way of visualizing the factorizations of 100 can be found here.
- Euler’s number $$e$$ is the protagonist of this short article about some of its properties.
- Scientific American has a nice blog post on the most mathematically perfect day.
- Ganit Charcha has a very well written post about the divisor function which would be very helpful for beginning elementary number theory students.
- An interview with Nira Chamberlain about how math is not just a tool for use but a confluence of beautiful ideas.
- Two comics on the occasion of $$tau$$ Day and 4th of July.
- Daniel McQuillan writes about some famous inequalities in mathematics and the intuition behind them.
- An interview with Siobhan Roberts, the author of John Conway’s biography.
- Here is a deceptively simple paradox from the financial arena.
- John Cook writes about integers whose last digit do not change when raised to the fifth power.
- Finally, an interesting mathematical puzzle created by Colin Beveridge.

Thanks to everyone who sent us the submissions, I had a great time hosting this carnival. The next carnival in August 2015 will be hosted by Nick at Data Genetics.

Managing Editor of the English Section, Gonit Sora and Research Associate, Cardiff University, UK.