Fesshole 🧻20h ago
My phone number is a 7-digit prime that shows up in the digits of pi. My husband's phone number is a 7-digit prime that shows up in the digits of e. We met when training students for the Maths Olympiad. The fess is how nerdy we both are.
Show threadNeal Walfield20h ago

@fesshole That the numbers are both prime is a cool coincidence, but all numbers show up in irrational numbers like pi and e.

Edit: We don't know that all numbers show up in irrational numbers; it's just a conjecture. Thanks to those who replied for clarifying (and see below for more details).

Show threadChaucerburnt20h ago
@nwalfield @fesshole that's actually not confirmed! Being irrational is not a guarantee that every digit sequence occurs; you can make an irrational with only 0s and 1s. It's generally *believed* that every finite digit sequence shows up somewhere in pi and e, but not proven.
Show threadJdeBP19h ago

@nwalfield

For the technically minded, the name for such numbers is 'normal numbers'. Not much is known about the relationship between the transcendentals and the normals, or even whether some common algebraics are normal.

So the thing about π at the end of Carl Sagan's Contact, if true, may be either profound or trivial.

@chaucerburnt @fesshole
#maths #mathematics #CarlSagan #pi

Show threadChaucerburnt19h ago
@JdeBP @nwalfield @fesshole "normal" is a stricter condition - it requires not only that every finite sequence appears, but that any two sequences of length n occur at the same frequency, for all positive integer n.
Show threadJdeBP19h ago

@chaucerburnt

The interesting question is whether it actually is stricter. It would certainly seem so on its face. But I don't know whether it is conjecture or proven that there's a difference; and I have long since learned to be wary about making claims about infinitely big things based upon intuition alone. (-:

@nwalfield @fesshole
#maths #mathematics

Show threadChaucerburnt
@JdeBP @nwalfield @fesshole write a decimal point, then for n = 1 to infinity: enumerate all n-digit sequences (takes a total of (10^n) n digits), then write a sequence of n! zeroes. Every sequence appears, but density of zeroes asymptotes to 1.
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