# 211

Set a digital clock to display in 24-hour (military) time. Each day, it will show you 211 prime numbers starting with 00:02 (2 minutes after midnight) and ending with 23:57 (3 minutes before the next midnight.)

Oh, and 211 is also prime, so 02:11 would be one of the 211 prime times you observe each day.

# Codes and Ciphers Teaching Resources Website

Somehow I found this fun website with various teaching resources using different coding and decoding methods: http://www.cimt.org.uk/resources/codes/?fbclid=IwAR2yX_yDK0UAmLB2acIgbk15wJMy_QXFJSuKaQOj3q-SlrFkuuuxpsEXoyI

# Incredibly difficult math puzzle

For math/puzzle enthusiasts (as well for as my own future reference): This was one of the most diabolically difficult puzzles that I’ve ever seen. The object: use the numbers 1-9 exactly once in each row and column while ensuring that the given arithmetical operation in each cage is also correct. Here it is. Fair warning: while most MathDoku+ puzzles take me 20-40 minutes to solve, this one took me over 3 hours (spread out over 5 days).

# Repunit prime

In the United States, today is abbreviated 10/31. Define the $n$th repunit number as

$R_n = \frac{10^n-1}{9} = 1111\dots1$,

a base-10 number consisting of $n$ consecutive 1s. For example,

$R_1 = 1$

$R_2 = 11$

$R_3 = 111$

$R_4 = 1,111$,

and so on.

It turns out that $R_{1031}$ is the largest known prime repunit number.

# Pizza Hut Pi Day Challenge: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on the 2016 Pizza Hut Pi Day Challenge.

Part 1: Statement of the problem.

Part 2: Using the divisibility rules for 1, 5, 9, 10 to reduce the number of possibilities from 3,628,800 to 40,320.

Part 3: Using the divisibility rule for 2 to reduce the number of possibilities to 576.

Part 4: Using the divisibility rule for 3 to reduce the number of possibilities to 192.

Part 5: Using the divisibility rule for 4 to reduce the number of possibilities to 96.

Part 6: Using the divisibility rule for 8 to reduce the number of possibilities to 24.

Part 7: Reusing the divisibility rule for 3 to reduce the number of possibilities to 10.

Part 8: Dividing by 7 to find the answer.

# Euler and 1,000,009

Here’s a tale of one the great mathematicians of all time that I heard for the first time this year: the great mathematician published a mistake… which, when it occurs today, is highly professionally embarrassing to modern mathematicians. From Mathematics in Ancient Greece:

In a paper published in the year 1774, [Leonhard] Euler listed [1,000,009] as prime. In a subsequent paper Euler corrected his error and gave the prime factors of the integer, adding that one time he had been under the impression that the integer in question admitted of the unique partition

$1,000,009 = 1000^2 + 3^2$

but that he had since discovered a second partition, namely

$1,000,009 = 235^2 + 972^2$,

which revealed the composite character of the number.

See Wikipedia and/or Mathworld for the details of how this allowed Euler to factor $1,000,009$.

# Factoring Mersenne “primes”

I love hearing and telling tales of legendary mathematicians. Today’s tale comes from Frank Nelson Cole and definitely comes from the era before calculators or computers. From Wikipedia:

On October 31, 1903, Cole famously made a presentation to a meeting of the American Mathematical Society where he identified the factors of the Mersenne number 267 − 1, or M67. Édouard Lucas had demonstrated in 1876 that M67 must have factors (i.e., is not prime), but he was unable to determine what those factors were. During Cole’s so-called “lecture”, he approached the chalkboard and in complete silence proceeded to calculate the value of M67, with the result being 147,573,952,589,676,412,927. Cole then moved to the other side of the board and wrote 193,707,721 × 761,838,257,287, and worked through the tedious calculations by hand. Upon completing the multiplication and demonstrating that the result equaled M67, Cole returned to his seat, not having uttered a word during the hour-long presentation. His audience greeted the presentation with a standing ovation. Cole later admitted that finding the factors had taken “three years of Sundays.”

# My Favorite One-Liners: Part 92

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

This is one of my favorite quote from Alice in Wonderland that I’ll use whenever discussing the difference between the ring axioms (integers are closed under addition, subtraction, and multiplication, but not division) and the field axioms (closed under division except for division by zero):

‘I only took the regular course [in school,’ said the Mock Turtle.]

‘What was that?’ inquired Alice.

‘Reeling and Writhing, of course, to begin with,’ the Mock Turtle replied; ‘and then the different branches of Arithmetic — Ambition, Distraction, Uglification, and Derision.’