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Fun with Maths – Why Seven is so Awesome

  1. Most people can generally hold around seven numbers in their working memory for a short period of time (Miller’s law), which explains why our telephone numbers are mostly seven digits (excluding the country and area codes).
  2. Several sleep studies have found that seven hours is the optimal amount of sleep, not eight!
  3. There are seven colours in the rainbow: red, orange, yellow, green, blue, indigo, and violet.
  4. The ‘Seven Seas’ (as in the idiom ‘sail the Seven Seas’) is an ancient phrase for all the world’s oceans: Arctic, North Atlantic, South Atlantic, Indian, North Pacific, South Pacific, and Southern (or Antarctic).
  5. There are seven continents in the world: Africa, Europe, Asia, North America, South America, Antarctica,and Australia.
  6. Seven is used 735 times in the bible (54 times in ‘Revelation’ alone)! If we include ‘sevenfold’ and ‘seventh’, the number jumps to 860!
  7. And of course, seven is a prime number. 😉

Happy Seven! 😀

Sponge ME, Maths Tuition (Singapore)

What are Prime Numbers?

Meet the Numeric Celebrity – Prime Numbers

That’s right, primes are quite the celebrity and not just in Hollywood movies. 😉  Here’s an excerpt of primes being featured in the movie, “Contact” where scientists discover an alien signal composed of… yes you’ve guessed it, prime numbers!

As seen in the movie, the aliens chose to send a long string of prime numbers to prove that their message was intelligent and not of natural origin. So why use prime numbers? What so special about primes?

What are prime numbers?

Primes are the building blocks of all numbers. Think of prime numbers as atoms, just like in chemistry where we say that a water molecule is formed from two hydrogen atoms and one oxygen atom (notated as H2O). Likewise, the number 12 is the product of the prime factors 2×2×3 (notated as 22 3). So just like water can be decomposed into hydrogen and oxygen, all numbers can be decomposed into primes. Here are a few more examples:

  • 8 = 2×2×2 = 23
  • 20 = 2×2×5 =22 5
  • 180 = 2×2×3×3×5 = 22 32 5

This process of decomposing a number into its prime factors is called prime factorisation (a topic to be left for another time). Like atoms, prime numbers can’t be decomposed further or rather can’t be divided further, like 2, 3, 5, 7, etc. In other words, prime numbers are only divisible by 1 and itself, and a number that has more than 2 factors is known as a composite number. For example:

  • 2 = 1×2 (2 factors only) → Prime
  • 3 = 1×3 (2 factors only) → Prime
  • 4 = 1×4 or 2×2 (3 factors) → Composite
  • 5 = 1×5 (2 factors only) → Prime
  • 6 = 1×6 or 2×3 (4 factors) → Composite

At this point, you may be wondering – what about the number 1? Is it prime? Well, 1 is somewhat of a special case. If you think about it, 1 = 1×1×1×1×1… and this is where things get a little crazy. If you were to just consider the number of factors 1 has, it’s 1, which is also itself! So… is it prime? There is certainly a little more than meets the eye. 1 used to be prime, but it’s no longer prime. Haha… and the story of primes continue to unravel. To find out more, watch the short video below, where James Grime the Numberphile, concisely explains the Fundamental Theorem of Arithmetic (don’t worry, it’s just a fancy name – watch the video and all will become clear) and how it applies to 1 and prime numbers.

Cool right? Okay, so we now know that 1 is neither prime nor composite. It’s just the lonely one. Awww… poor 1. 😢

Well, is that all there is to prime numbers? Far from it! Here are a few more observations and interesting facts about prime numbers:

  • I’m sure you’ve noticed this. 2 is the only even number that is prime. The rest of the prime numbers are odd.
  • As numbers get larger, primes become less frequent and twin primes (see below) get even more rare.
  • In any case, we’ll never run out of prime numbers, as they are infinite. Any idea what’s the largest prime number ever discovered to date? Watch the final video below to find out.
  • Twin primes are pairs of primes that differ by two. The first twin primes are {3,5}, followed by {5,7}, {11, 13} and so on. It has been conjectured (meaning it’s never been proven) that there are infinitely many twin primes. This is known as the twin prime conjecture, a.k.a. Euclid’s twin prime conjecture.
  • Prime factorisation is hard work and when numbers get extremely large, you can imagine how tedious and slow it’ll be. ?
  • On top of this, primes do not have a pattern we can easily decipher, meaning there is no easy way to tell when the next prime number will appear. But that’s actually a blessing in disguise. Why? Read on to find out more.

Why are prime numbers so important?

Did you know that prime numbers are worth billions of dollars? 😲  Why are prime numbers so valuable to organisations, government agencies and companies like Apple, Google, eBay or Visa? Wondering how numbers can be worth even a single cent? Well, though prime numbers have little value in themselves, they are used in every credit/debit card transaction, including ATMs, online payments and even trading (e.g. stocks and shares) transactions totalling billions of dollars every day. In fact, prime numbers power the mathematics behind the cryptography (used for cyber security) of your WIFI connections, email accounts, blogs, Facebook, Twitter, etc.

To find out how primes combined with the difficulty of factoring large numbers are used to protect and secure our emails and payment transactions, please watch the short video below.

Aren’t prime numbers just fascinating? As Carl Sagan, author of the science fiction novel, “Contact” so eloquently pointed out – there is a certain importance to the status of prime numbers as the most fundamental building block of all numbers, which are in turn themselves the building blocks that help us understand our universe. 🤔  Regardless of how an advance alien life form may think or look like, one thing is for certain, if it understands the world around it, it most certainly understands the concept of primes.

Hope you found this article insightful and educational. Happy maths! 😁

Sponge ME, Maths Tuition (Singapore)

Oh… and if you are interested to find out what is the largest prime number ever discovered to date (Jan 2016), here is Matt Parker on the latest Mersenne Prime that holds the envious world record. Who knows? Maybe you might be the next record breaker for finding the “world’s largest prime”. Find out how it’s done and more in this video. Enjoy! 😉

Personal Recount Model Essay #2

Write about a stranger who left a deep and lasting impression on you because of his or her actions.

He came, he saw, he helped. Then, he left without even telling us his name. To this day, I still remember his face and mannerism vividly. How could I ever forget him and the kindness he showed us?

It was during the March holidays and my mother and I were on our way to Malaysia to visit my aunt. We were in high spirits and the mood was set for an enjoyable day. Unfortunately, halfway through our road trip, one of our car tyres was punctured in the middle of the highway. As my mother did not know how to change a car tyre, we had no choice but to seek help. For almost an hour, we waved at every passing vehicle but no one slowed down, much less stopped. As if the situation could not get any worse, the weather changed suddenly. Thunder rumbled and lightning cracked open the ashen sky. Dark ominous clouds gathered overhead as rain threatened to fall.

“Where are all the helpful people! I can’t imagine being stranded here for hours!” I began to whine.

Just then, a screech of brakes was heard.

A battered old truck stopped a few centimetres ahead of me and out came a towering man with broad muscular shoulders and strong heavily-tattooed arms. His weather-beaten skin was as coarse as an alligator’s and he had a pock-marked face that looked like a pimple plantation. His eyes were so tiny that they were almost non-existent and his bulbous nose had the shape of a large garlic clove. To put it plainly, he was ugly and formidable looking.

“Do you need help?” the intimidating stranger asked in a gruff voice.

An irrational fear overwhelmed me, causing my heart to palpitate so fast that it might just leap out of my mouth. Instinctively, I moved behind my mother for protection.

“Ermh… yes please. Our tyre is punctured,” my mother muttered hesitatingly after what seemed like eternity.

Without a word, the stranger walked back to his beat-up truck and took out a toolbox. Taking the spare tyre from my mother, he flashed us an enigmatic smile and started work. We stood near him uneasily, half thankful and half suspicious of his motives.

Minutes passed and a gentle drizzle began to drift down from the darkened sky. Heat was instantly radiated from the ground as the light drizzle cooled the surroundings. My mother immediately told me to get into the car while she took an umbrella to place over the stranger to prevent him from getting wet. However, as the rain got heavier, my mother also came into the car at the stranger’s bidding.

“It’s okay. There’s no point in you standing here and getting wet too,” he said, his coarse voice muffled by the pelting rain.

For the next ten minutes or so, we sat silently in the car and watched the good Samaritan fix our tyre. He was focused on the task even though the wind had grabbed the umbrella and he was drenched to the skin.

When he was finally done, he simply knocked on the car window and said casually, “Your car is good to go.”

Before we could utter a word of thanks, he turned around and hopped into his truck. Then he left as quickly as he came. Just like that.

This mysterious man has left a deep and lasting impression on me because he has taught me two valuable life lessons. Firstly, he has taught me not to judge a book by its cover. When I first saw him, I instantly associated him with criminals. Nevertheless, he turned out to be the kindest person I have ever met. Thanks to him, I no longer form an opinion about others just because of the way they look. More importantly, he has taught me what it really means to help others. There are people out there who are willing to help those in need without asking for anything in return. These are the people who make the world a better place with their kindness and consideration. Although our encounter was brief, I will never forget this memorable character who gave my mother and me a helping hand and so much more.

Secondary 2, 2015, English Tuition