*Seventy-two** is the sum of four consecutive primes (13 + 17 + 19 + 23), as well as the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19). *

*The product of 8 and 9, 72 is a pronic number.*

* The sum of Euler’s totient function φ(x) over the first fifteen integers is 72. There are 17 solutions to the equation φ(x) = 72, more than any integer below 72, making it a highly totient number.*

* 72 is the smallest number whose fifth power is the sum of five smaller fifth powers: 19*^{5}* + 43*^{5}* + 46*^{5}* + 47*^{5}* + 67*^{5}* = 72*^{5}*.
*

*The sum of the eighth row of Lozanić’s triangle is 72.
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*In a plane, the exterior angles of a regular pentagon measure 72 degrees each.
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*In base 10, the number 72 is a Harshad number.*

All of the above is from Wikipedia. Why did I google 72? Because as I was lamenting the sum of years on my approaching birthday, a friend commented that it was a “very good number”. Yes, I knew that lots of numbers go into 72 because I belong to a generation that learnt multiplication tables by rote and began most maths lessons in primary school by reciting them. Does it sweeten the bitter pill to know that one has reached an “interesting” figure agewise? Maybe, for some.

Anyway, this Wikipedia information gave me a few more things to look up. As is so often the case with Google, whatever it may be accused of, it does turn up some fascinating stuff and is very addictive.

I did know what a prime number is, and there is something vaguely pleasing about 72 being the sum of so many consecutive primes, though I can’t explain why it should produce that effect. Perhaps that is what drives true mathematicians? The term *pronic* or *rectangular number* was new to me and the concept gives me a strange satisfaction as I visualise the neat oblongs. Yes, maybe I have the heart of a mathematician after all, in spite of being dysnumeric.

The angles of a pentagon – that’s clear, I remember that from my school days. I admire the brainpower of whoever figured out that line about the fifth powers, because that is something that would never have occurred to me in a million years. And I pat myself on the back because I understand it. However, now comes the real test.

I have O-level maths, but my maths lessons never included such abstruse matters as calculus or Euler’s totient function, which sounds daunting before you start. Wikipedia’s summary of it left me feeling dizzy, though my granddaughter dismissed it airily: “Oh Euler’s phi function …” and gave me a rundown on Euler, whose face I know because he features on a Swiss bank note. I had also heard of Euler’s line, which divides a triangle, so I wasn’t totally ignorant of the name.

I have read that Wikipedia entry on Euler’s totient function at least half a dozen times now, and it still leaves me with vertigo. I moved on to Losanic’s triangle, and my vertigo began to turn to nausea so I quickly looked up *Harshad number*, hoping to find an antidote. Here at last some information I could stomach: the word Harshad comes from the Sanskrit and means “joy-giver”. Maybe it would give **me** some joy, too? *A number divisible by the sum of its digits.* YES! I understand that! JOY! However, the mathematical examples that followed may as well have been written in Sanskrit for all the sense they made to me. My heart sank. Vertigo returned. I am not a mathematician after all.

QED.

I am no whizz on maths myself

😀

Just a little twist on the 72 or its reverse digits of 27.

My mother was born in ’27. I was born on her birthday in ’54. She was 27.

In ’81, I was 27 (her birth year), she was 54 (my birth year), and the sum of our ages was 81, (the year at the time).

Also until the turn of the century the sum of our ages always added up to the same as each other and the same as the year eg: When I was 27 (2+7 =9), she was 54 (5 + 4 = 9), in ’81 (8 + 1 = 9). That worked every year until ’99 (9+9 = 18; 1 + 8 = 9); I was 45 (4 + 5 = 9); Mum was 72 (7 + 2 = 9). Are there is that number 72 again!

Numbers are fun 🙂

That is lovely!

Amazing – for a couple of minutes I thought this could be another one of your enlighting articles. As I arrived at Euler’s totient function I started zoning out and stayed in “outer space” – 🙂 I always thought there is balance in the universe – mathematics for some people and art for others… I do not fall into the first category. But amazing at what you come up with.

Maths (and physics) only work for me if I can visualise the concepts. But I have problems with numbers – am dysnumeric to a certain extent – and that makes it tough!