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The Big Internet Math-Off 2024, Round 1, Match 1
The Big Internet Math-Off 2024, Round 1, Match 1 – Here's the first match in this year's Big Internet Math-Off. Today, we're pitting Katie Steckles against Benjamin Dickman. Take a look at both pitches, vote for the bit of maths that made you do the loudest "Aha!", and if you know any more cool facts about either of the topics presented here, please write a comment below! Overview of the 2024 edition.
Previous editions:
posted by Wolfdog on Jul 01, 2024 at 3:35 AM
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Steckles [✓].
I was primed for her finding something interesting about chunks of consecutive numbers [in the digits of π] by yesterday's Numberphile [James Grime YT 14m] about Erdős–Woods Numbers https://oeis.org/A059756.
posted by BobTheScientist at 4:16 AM
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the link out about Roger Apéry, apéryodical *bemused*, reminds me of memorials for Ludwig Boltzmann [atlas obscura] & Erwin Schrödinger ([medium:] Schrödinger's could be thought of as a puzzle, perhaps?) Shakespeare was more direct [Cañada college]
posted by HearHere at 4:41 AM
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or, maybe, *indirect [xkcd]
posted by HearHere at 5:21 AM
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If you think those smartie as foo math gals&guys have the last word on truth, just dig into ABC
posted by sammyo at 7:59 AM
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Steckles [✓]
prime contender, for sure :-)
posted by HearHere at 10:53 AM
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Ah, I vote for Dickman, because it actually gives an interesting and surprising answer to a question. Steckles's study was interesting, but it leaves the really big question open: is pi (or any normal number) chunkable into an arbitrarily large number of primes in base 10? She showed 9 chunks, and gave a good argument why the 9th chunk is big, but is there a 10th chunk? Or an 11th? And if both of those are "yes", is there a reason why you can be certain the nth chunk exists in general? 'Cause it's quite possible that after a certain point the unlikelihood of a k-digit prime counters the fact that there are an infinitude of possible sizes k, so that the search for a particular chunk ends up never ending. But it's also possible that the reverse is true; even though primes are rare, tacking random digits onto the end of a number is guaranteed to eventually give you a prime number, because all those tiny probabilities don't actually diverge fast enough. Its an interesting question and left frustratingly unexplored. Also, it seems like it might well have different answers in different bases; a base like 60 is a very bad one, because only 16 of the possible final digits base 60 (26.7%) are possible last digits of a prime number with two or more digits (versus 40% for base 10), while base 61 is very good; every final digit except zero is possible for a prime (98.3% of them). It's possible the base is irrelevant (constant multipliers in the limit of an infinite probability calculation resulting in 0 or 1 usually don't actually affect the outcome), but maybe it isn't. As I said, interesting questions but much towards answering them.
posted by jackbishop at 2:12 PM
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I voted for Steckles because her post left me with those questions. :-)
I doubt anyone knows whether pi can be chunked into primes indefinitely, but the probabilistic argument suggests a random stream of digits almost certainly can be, and that the average length of those primes will tend toward infinity.
posted by aws17576 at 9:54 PM
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