What are some things we can prove they must exist, but have no idea what they are?

Examples I can think of:

- Values of the
Busy beaver function: It is a well-defined function, but not computable.- It had been long known that there must be self-replicating patterns in
Conway’s Game of Life, but the first such pattern has only been discovered in 2010- By the
Well-ordering theoremunder the assumptions of the axiom of choice, every set admits a well-ordering. (See also Is there a known well ordering of the reals?)

**Answer**

Not sure if this satisfies the requirement that we “have no idea what they are”, but the extremely strange Mill’s constant seems worth mentioning here: There is supposed to be some real number r>0 with the property that the integer part of r3n

is prime for every natural n. It is not known if r is rational and as far as I know not even a numerical approximation of r is possible without assuming the Riemann hypothesis.

Source: Wikipedia

**Attribution***Source : Link , Question Author : Loreno Heer , Answer Author : Ooker*