Happy Birthday!
Possibly, congratulations on it maybe being your birthday.
Although statistically speaking it is very unlikely today is your birthday.
If you run the numbers only 0.247% of all days are your birthday.
I guess a more positive way to look at it is today you are currently enjoying on average
0.274% of your birthday.
And even, what are you celebrating on a normal birthday?
Approximately one lap around the sun?!
Because of leap years it doesn't really line up anyway.
The best you can say is for a standard orthodox birthday simply celebrating the fact that
the calendar on that day bears a striking resemblance to what the calendar looked like
when you first emerged from the womb.
We can do better than that!
Today for example I am exactly eleven thousand nine hundred and eighty seven days old, that's
a prime number, today is my prime numbered birthday.
That's much better it is far more mathematically interesting to celebrate prime numbers of
days than orbits around the sun.
Even better today is my one thousandth four hundred and thirty eighth prime birthday.
Prime birthdays come far more frequently they're more mathematically interesting and there's
more of them.
In fact if you approximate a human as living around about a hundred years so you go from
zero to ten to the two, across those hundred years, you get thirty six thousand five hundred
and twenty four days.
It does vary ever so slightly depending on when you were born and where the leap years
are.
And as you come in and out of phase with them, according to birth, the numbers change ever
so slightly.
But on average you're gonna get three thousand eight hundred and seventy one prime numbered
birthdays across a hundred years of existence.
That's ten point six per cent of all days being your prime birthday.
As you get older your prime number birthdays will become less common that's just because
as numbers get bigger fewer of them are prime numbers.
To start with the going is pretty good.
For the first ten years of your existence, from zero to ten, which covers about three
thousand six hundred and fifty two days, of those, five hundred and ten of them will be
prime.
That's fourteen percent.
That's not bad, but middle age things aren't so good.
Your fifth decade which is forty through to fifty, the same number of days but only three
hundred and eighty three of them are actually prime numbers, that's ten point five percent.
It's dropped a fair bit and by the end of the hundred years from ninety through to a
hundred you will only have three hundred and forty seven prime numbered days in that decade
that's nine point five percent.
Which is not to say though that the prime numbers get consistently worse, even though
overall they do, prime numbers are pretty random and they can fluctuate a decent amount.
For example during your thirties when you are thirty one for a whole year you don't
get many prime numbered birthdays you only get thirty three prime days that's nine point
zero four percent.
That's a pathetic percentage as far as prime numbers go, however the exact next year the
entire time you are thirty two, the heyday of your prime birthdays, you get forty two
primes in that year, that's eleven point five one percent.
That's much better.
Now overall it does get gradually get worse and worse and worse and if humans live beyond
a hundred it will continue to tail off.
In my approximation in your last year of existence from ninety nine through to a hundred eight
point seventy seven percent of those days will be prime numbered.
Now should you be wondering now wait a minute, what if you live to be older than a hundred?
Do things continue to get bad?
Yes, they do, I've checked the numbers.
Should you live to be a thousand?
For a start you should be absolutely ecstatically happy and then you should be rapidly depressed.
Because for that last year of your life between nine hundred and ninety nine and one thousand
only eight point two percent of those days will be prime.
Should you wonder about ten thousand, I've done the numbers for that as well!
Between the age of nine thousand nine hundred and ninety nine and ten thousand, only six
point zero three percent of those days are prime and I also double checked for a hundred
thousand.
So between ninety nine thousand nine hundred and ninety nine and a hundred thousand years
old only five point seven five percent of those days are prime and it continues to get
worse.
Should you want to know what it is for a million you're gonna have to work it out yourself
it was at this point my prime numbered birthdays programme crashed and I decided to do something
else with my life.
Should you work it out though, please do let me know.
One very valid critique of the prime numbers birthday thing is that they get a little bit
too frequent.
If you're having a birthday every ten days for the entirety of your life the novelty
will wear off but thankfully maths still comes to the rescue.
There are mathematically interesting birthdays which are far less frequent.
For example do you know when your one billion second birthday was?
I know when mine was!
I had a party and everything, I had a cake admittedly I had one candle per billion seconds
but still the point remains, what about your one thousand month birthday?
What about your fifty thousandth hours birthday?
In fact there are these amazing milestones that people hit and they never notice.
So what I've done is gone through and calculated all the nice kind of whole numbered multiples
of convenient time intervals so you can then celebrate it.
Now I can't give you exact dates that's mainly because I don't know when your birthday is,
sorry, and also because it depends ever so slightly on when you're born compared to leaps
years so it depends where you are in a leap year cycle and how many days you have at each
particular age that you're at.
But what I can do is give you rough ages.
I can tell you what age in standard earth years you would be when the more interesting
mathematical birthdays will occur.
And after that it's up to you to find them.
So I'm going to rattle through this list in semi fast fashion.
Simply listen out for any years which are in your near to immediate future and if you
look at the link that I'll put underneath this video if you go on to some of those,
put in your birth date exactly, hopefully to the nearest second, if you're not sure
when that was because your memory was a bit hazy just ask your mum, she will remember!
You can then find your exact mathematical birthdays so you can celebrate them in fashion.
Here we go: We'll start with months because that is the
largest time interval, you will be twenty when you have your two hundred and fifty month
birthday.
You'll be forty one when you turn five hundred months and at some point when you're sixty
two you'll pass seven hundred and fifty months and when you're eighty three you'll have your
one thousand month birthday.
Moving down to weeks.
When you're nineteen you'll pass a thousand weeks old, when you're thirty eight you'll
go straight past two thousand weeks, at some point when you're fifty seven you go pass
three thousand weeks, four thousand weeks is when you're seventy six and five thousand
weeks is some point when you're ninety five.
Coming down to days, these are much less common these are absolutely worth celebrating.
You turn ten thousand days at some point when you're twenty seven.
I remember that!
What a hoot!
You hit twenty thousand days when you're fifty four, still looking forward to that and you
hit thirty thousand days when you're eighty two.
You only get three of these days, don't miss them!
Now beyond that we're getting down to the realms of hours.
You turn ten thousand hours when you're eleven, most of you have probably already missed that.
Ok, coming up you might have twenty thousand hours when you're twenty two, thirty thousand
hours is when you're thirty four, forty thousand hours is when you're forty five, fifty thousand
hours is when you're fifty seven, oh and if you remember fifty seven is when you turn
thirty thousand weeks.
What a year!
Now beyond that you get sixty thousand hours when you're sixty eight, seventy thousand
hours when you're seventy nine, and eighty thousand hours when you're ninety one.
Coming down now to minutes.
You turn ten million minutes when you're nineteen, oh which you may remember is when you turned
one thousand weeks old.
What a coincidence.
You hit twenty million minutes when you're thirty eight, oh which you may remember that
was the same age when you turned two thousand weeks old.
You hit thirty million minutes when you're fifty seven; oh you remember that the same
age you hit three thousand weeks.
Ok, there is a pattern here it's because you have a nice standard multiple of minutes in
weeks, if you work it out you can see why you always get the same years every time.
Although fifty seven has the added bonus of when you're fifty thousand hours old.
That's three birthdays in the same year!
What a year!
Fifty seven!
Now of course beyond that you'll hit forty million minutes when you're seventy six and
you'll hit fifty million minutes when you're ninety five.
Now, seconds.
You get half a billion seconds when you're fifteen, you get one billion seconds when
you're thirty one.
Do not miss that birthday.
You get one and a half billion seconds when you're forty seven.
You get two billion seconds when you're sixty three, and you get two and a half billion
seconds when you're seventy nine.
Oh which is the same year when you get seventy thousand hours.
And finally ninety five not only do you get three billion seconds you also get five thousand
weeks and five million minutes all in the same year.
What a year!
Not since you were fifty seven have you had that much fun in the same year!
Ok so those are all the nice round number intervals you could celebrate but yes it's
all a little base 10-y.
So we've got one last thing here a bit of a reoccurring favourite at Number Hub -- Pi.
Why just celebrate the rational number of years?
Why not celebrate some irrational birthdays?
Pi years is three years and fifty two days so just under two months, so you can actually
celebrate your multiple of Pi birthday.
So you turn ten Pi when you are thirty one years and a hundred and fifty two days old.
You turn Pi cubed birthdays when you're thirty one years and three days old.
That's easy to remember, three days after your thirty first birthday you turn Pi cubed.
I remember that too!
And finally the most irrational of all birthday you're gonna come across, Pi to the power
of Pi!
Pi to the Pi is thirty six years a hundred and sixty nine days when measured in standard
years, which means you can have the most irrational birthday with a transcendental party that
you will ever have.
A final word in all of this.
Most people miss all of these wonderful mathematical birthdays; in fact, you've possibly missed
some yourself.
What you need to do now is look up the website I've put in the description, mark these in
your calendar, preferably some kind of electronic calendar, and then make sure an alarm goes
off to remind you a significant mathematical milestone is coming up.
Even more important though, look up your friends birthdays because they are probably going
to miss these as well.
Other people who aren't quite as mathematically excited as we are don't even notice when a
billion seconds slips by.
So put your friends' birthdays in the same website and mark them down on your calendar
and then surprise them with a happy billionth second card on the appropriate day.
Because friends don't let friends miss mathematical milestones.