Everyone’s heard of the number 3.141592…, right?

And you probably know that is not a rational number (i.e., a quotient of two integers, like 7/3). Unlike a rational number, whose decimal expansion is eventually periodic, if you look at the digits of they seem random,

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482…

But are they really? No one really knows. There’s a paper that explores the statistics of these digits using the first 22.4 trillion digits of . Does any finite sequence of *k* digits (say, for example, the *4*-digit sequence *2016*) occur just as often as any other sequence of the same length (say, *1492*), for each *k*? When the answer is yes, the number is called ‘normal.’ That is, a **normal number** is a real number whose infinite sequence of digits is distributed uniformly in the sense that each digit has the same natural density *1/10*, also all possible * k*-tuples of digits are equally likely with density

*, for any integer .*

`1/k`The following simple problem is *unsolved*:

**Conjecture:** * is normal.*

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