I thought pi hadn’t been proven to be normal, only conjectured to. My phone number isn’t in the digits of pi that we’ve discovered so far, for example: https://www.angio.net/pi/
Plot twist: the websites that check if a given number has been found in pi are actually just data mining operations looking for credit card numbers and phone numbers.
Chaitin’s constant also known as Chaitin’s Ω is transcendental, uncomputable and algorithmically random. Also normal in every base. I don’t know how or what any of it means, but it’s a probable, normal number.
is 200m what’s been discovered, or just what was worth putting into this program? Not a huge expert but I thought it’s all fairly easy to get the next number of pi, just seemingly never ending.
We currently know about 202 trillion digits of pi. As for your other question: it is easy to get the next digit of pi from a “mathematical” point of view. By this I mean that we know functions that will approximate pi with as much precision as we want, but actually having a computer do it is very hard. The digits we know today took 3 months and needed 1.5 petabytes of high end storage.
Yes, I’m aware of that, but being irrational alone is not sufficient. There are an infinite number of irrational base-10 numbers that only contain combinations of 0 and 1, for example, and none of them will contain my phone number, credit card, etc.
Not all irrational numbers are normal numbers, and only normal numbers are guaranteed to behave as described in the OP.
I thought pi hadn’t been proven to be normal, only conjectured to. My phone number isn’t in the digits of pi that we’ve discovered so far, for example: https://www.angio.net/pi/
Plot twist: the websites that check if a given number has been found in pi are actually just data mining operations looking for credit card numbers and phone numbers.
That did occur to me, so I only gave them my old number.
Well obviously that’s not in pi. Pi only tracks current phone numbers.
There is a website that just has like, a million digits of py in plai text, you could go there and ctrl+f
I checked a couple but none were found if I included the area code.
Based on my sample size of half a dozen phone numbers, it doesnt seem to have numbers once they are more than 8 digits.
Seems like there should some formula to determine how long the normal number needs to be to have all digits go to a certain length.
Reminds me of the formula for calculating the shortest path to watch all episodes in a tv series in all possible orders.
Sorry for the AI slop. I am not an artist and just thought this was kind of funny. I like that Ω is hidden in their hairstyle.
Chaitin’s Ω: Not just transcendental but uncomputable and algorithmically random. Also normal in every base.
Tap for spoiler
What does Omega mean?
Chaitin’s constant also known as Chaitin’s Ω is transcendental, uncomputable and algorithmically random. Also normal in every base. I don’t know how or what any of it means, but it’s a probable, normal number.
is 200m what’s been discovered, or just what was worth putting into this program? Not a huge expert but I thought it’s all fairly easy to get the next number of pi, just seemingly never ending.
We currently know about 202 trillion digits of pi. As for your other question: it is easy to get the next digit of pi from a “mathematical” point of view. By this I mean that we know functions that will approximate pi with as much precision as we want, but actually having a computer do it is very hard. The digits we know today took 3 months and needed 1.5 petabytes of high end storage.
Apparently it’s been calculated to trillions of digits so a bit lacking.
The search on that length would need an optimized index.
Pi is provably irrational
Yes, I’m aware of that, but being irrational alone is not sufficient. There are an infinite number of irrational base-10 numbers that only contain combinations of 0 and 1, for example, and none of them will contain my phone number, credit card, etc.
Not all irrational numbers are normal numbers, and only normal numbers are guaranteed to behave as described in the OP.
It doesn’t contain your phone number when read as a base 10 number! Checkmate, I got your phone number!
Sorry…
How about if it’s read as a base pi number?
🙀