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?
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.