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Number 6: From sexy primes to the first perfect number

A number so sexy it's perfect. In conversation with AFLW's Daisy Pearce. A chance to navigate the Milky Way. And raising over $70,000,000 by not drinking.

Give up the booze and help us raise millions. In just a couple of weeks we will be starting the 15th Dry July. What began as a talkback idea on my ABC 702 breakfast radio show has become an annual institution, raising over $70 million for adults living with cancer. Join me and thousands more in going dry for a month. Going beyond just the sobriety and raising money gives an even greater sense of purpose. So hop aboard and sign up, or if you can’t commit yourself, feel free to throw a few dollars my way here. Dry July – I’ll not drink to that.

Six is sexy

When two prime numbers differ by 6 – for example 13 and 19, 31 and 37, 37 and 43, and so on – such pairs are called sexy primes. That's because the Latin prefix for 6 is "sex". A triple like 7,13,19 is called a sexy triplet. There are 8 more sexy triplets involving numbers less than 200. Can you find them? (And if that’s got your heart racing, just wait until you discover why six is perfect further down the page!)

Enjoy these fascinating numerical facts about 6!

Spicy contention Twitter’s @qikipedia recently pointed out “Schwartz’s Chinese 5 Spice powder contains 6 spices”. In addition to star anise, fennel, cinnamon and cloves, if you count ginger, pepper, garlic and onion as spices, you could argue it contains 8!

From sex to hex The Latin prefix for 6 is “sex”, hence the remarkably rare birth of sextuplets* and the sixth month of the year being once called Sextilis. The Greek prefix for 6 is “hex”, hence a 6-sided shape is called a hexagon.

I'll play that! If you’re playing a board game and really want to nerd out your mates, just say “pass me the hexahedron”. They will look at you bemused until you explain that’s simply another word for a cube which is the shape of a typical six-sided dice.

* 1 in 4.7 billion chances according to this ABC story

INSPIRATIONAL THINKERS & DOERS - Daisy Pearce, Trailblazing the AFLW

As the father of two daughters and now a stepdaughter thrown into the deal, I think often about diversity and the opportunities afforded to young women and girls. Recently I interviewed Daisy Pearce who is a trailblazing AFLW player (and wears the number 6 guernsey for Melbourne Football Club!!!) as well as a hero to many. Daisy recalls that when she first moved to Melbourne she didn’t even know if women’s football was played there. The role model she’s since become just didn’t exist back then. Daisy also points out that far from the AFLW becoming an overnight sensation as many might believe, there was a solid decade or more of behind-the-scenes lobbying and sheer hard work involved.

Her story reminds me of world-class cricketer Usman Khawaja, a Muslim who emigrated from Pakistan to Australia at age five. Despite loving cricket as a boy, he could not see himself represented in any high-profile Australian cricketers. Khawaja is now a wonderful role model to countless youngsters and a passionate advocate for diversity in cricket.

Daisy, who is pictured above with my elder daughter Ellie – you ROCK!!!

Six is perfect

The factors of 6 – which means the numbers which divide into 6 – are 1,2,3 and 6. When added together (apart from 6 itself), we get 1 + 2 + 3 = 6. Wow! This doesn’t happen all that often. In fact it’s so rare that the Greeks called numbers like 6 perfect numbers. (Factors that add up less than the number are called deficient e.g. for the number 10 we get 1 + 2 + 5 = 8. Factors that up to more than the number are called abundant e.g. for the number 12 we get 1 + 2 + 3 + 4 + 6 = 16.) The next perfect number after 6 is 28. You should be able to convince yourself of this with 1 + 2 + 4 + 7 + 14 = 28. Why not grab a piece of paper and a pen and check that the numbers 496, 8128, 3350336 and, if you’re feeling lucky, 8589869056, are perfect numbers?

Awesome conversations - and a promo code!

If you’re in Sydney and keen to watch a fun and fascinating conversation, get along to the Judith Neilson Institute which supports quality journalism and great ideas. On Thursday June 30, the amazing Prof. Veena Sahajwalla will explain how we could live in a world without waste. Then on Wednesday July 27, Prof. Naomi McClure-Griffiths will take us on a tour of the Milky Way. These two incredible women will enthral and entertain, and then answer your probing questions. As a special thank you to readers of #number006, if you’d like tickets for under $10, use the promo code ADAMSPENCER50 here Yours in numbers, Adam


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