Today, we dive into the mesmerizing realm of prime numbers—those unique integers that can only be divided by one and themselves.
This infinite series kicks off with 2, 3, 5, 7, 11, and 13, and continues infinitely.
Mathematical Puzzles
Our journey starts with an intriguing mathematical puzzle from UK-based writer and former math educator, Steve Thompson.
He explores this theme in his recent thriller, Prime Target, which tells the story of a mathematician whose deep dive into prime numbers leads to surprising consequences.
Let’s begin with the first of our challenges:
- 1.
Last Digit Challenge
Think you can figure out the last digit of (3^{1,000,000}) without your calculator?
Now, let’s move on to a puzzle that Thompson holds dear.
- 2.
The Convenience Dilemma
Picture this: A customer strolls into a convenience store and picks up four items.When it’s time to pay, the cashier informs them that the total is £7.11.
The amused customer notes this fits nicely with the store’s name.
However, in a twist, the cashier reveals he multiplied the prices of the four items together.
This leaves the customer puzzled, who questions why addition wouldn’t be the right method.
The cashier insists that both methods yield the same total.
Can you work out the individual prices of the items? Hint: One item costs £3.16, and the rest can be divided by 5p.
The Significance of Prime Numbers
The concept for Prime Target originated about 25 years ago when Thompson served as the head of mathematics at a Kingston-upon-Thames grammar school.
During that time, science author Simon Singh visited to deliver a lecture about the use of prime numbers in cryptography and their significance in securing data online.
Prime numbers are fundamental to mathematics because every integer can be uniquely expressed as a product of prime factors.
For example, 100 can be broken down into (2 times 2 times 5 times 5), while 102 can be represented as (2 times 3 times 17).
However, the seemingly random distribution of prime numbers adds an element of intrigue.
This randomness is what makes them useful in data encryption—an unexpected pattern could compromise security, so the absence of a predictable sequence is crucial for protecting our online information.
From Math to Media
Thompson found himself captivated by this notion, pondering the slim chance of uncovering a sequence that has eluded mathematicians for centuries.
The absence of a discernible pattern is a cornerstone of modern digital security, and he realized that if such a predictable order were to appear, it could undermine the very foundations of online safety.
Inspired by Singh’s lecture, Thompson eventually transitioned from teaching to playwriting.
He gained recognition as a screenwriter, creating beloved series such as Sherlock and Doctor Who.
Nevertheless, his fascination with prime numbers never waned, culminating in the release of Prime Target on Apple TV+, which has garnered positive reviews.
Both challenges above highlight the prime number three, featured prominently in Thompson’s favorite conundrum.
While the first challenge requires some mental math, the second allows for the use of a calculator to tackle the prime factors of a larger total.
Feel free to join the conversation about your favorite prime numbers! Since 2015, I’ve been sharing a captivating puzzle every other week and am always on the lookout for more interesting challenges.
If you have a suggestion, I’d love to hear from you via email.
Source: Theguardian