Fesshole 🧻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.
silver moats@fesshole probably ill-conceived question from a non-maths student: if pi and e are never-ending numbers, does that suggest that any arbitrary 7-digit sequence has an equal likelihood of showing up at some point? non-repeating or prime sequences more probable than 7777777?
Nathan A. Stine@silvermoats @fesshole math degree here. If a number goes on forever and does not repeat in some cycle, any 7 digit sequence will be in the number. The number goes on forever so if you haven't found it yet, you just need to look further.
@stinerman @fesshole thanks, that was my intuitive understanding but OP got me wondering about the implications - not to get too pedantic though, assuming they're referring to a limited # of digits within which such a sequence could be observed as novel.
@stinerman @fesshole @fesshole I see this was covered earlier, couldn't view the replies on mobile for some reason
Howard Cohen
Anton Piatek@stinerman @silvermoats @fesshole am on another thread discussing this. Is it proven?
Intuitively I feel it should be true, but I wonder if there's a proof of it
Intuitively I feel it should be true, but I wonder if there's a proof of it
@sldrant @silvermoats @fesshole I don't know of a rigorous proof, but it's almost certainly likely to be true.
@stinerman @sldrant @fesshole depends on how strictly you define a 'non-repeating' sequence maybe? but you can also define infinity as containing every possible permutation, so with that in mind the occurrence of 7 consecutive digits doesn't seem all that improbable
Michael WestergaardNobody knows, but it seems like in this case the answer is yes.
7-digit sequences does not have to show up in irrational/non-ending numbers. For example, 0.101001000100001000001… is irrational (it never repeats as the sequence of 0's increase by one between each 1) but contains no sequences with the digit 2, for example.
It is possible to have numbers where each number sequence shows up, but with unequal probability. If they show up with the same probability, the numbers are called normal (en.wikipedia.org/wiki/Normal_number). This is very hard to prove, and it is not known whether π or e have either of these properties.
7-digit sequences does not have to show up in irrational/non-ending numbers. For example, 0.101001000100001000001… is irrational (it never repeats as the sequence of 0's increase by one between each 1) but contains no sequences with the digit 2, for example.
It is possible to have numbers where each number sequence shows up, but with unequal probability. If they show up with the same probability, the numbers are called normal (en.wikipedia.org/wiki/Normal_number). This is very hard to prove, and it is not known whether π or e have either of these properties.