I am searching for a mathematical conjecture that is true until something like n = 117, or n = 127, or a number close.
It is an equality, a formula implying calcultations to the power of n, IIRC.
What is the name of this conjecture ?
Why do I search for this formula ?:
I had read an article a few years ago that was discussing about experiments around the validation of a theory in Science, namely in Physics.
The example of this conjecture was given so as to convince that you can choose to repeat an experiment with different parameters a certain number of time, ultimately in the end, it does not give the entire certainty a physical theory is true: it just happens we still haven't found any outlier measurement that contracdicts the physical theory.
As a matter of fact, we can test this mathematical conjecture for the first 127 integers, which is a bunch of times, and believe it is always true, whereas it is false for all n.
I would like the name of it so as to be able to name it / source it in discussion.
Does it ring any bell for you ?
Well, we would have to define what exactly counts as a "conjecture". You can find a trivial example in something like:
"I conjecture that every positive integer can be expressed uniquely by 7 binary digits", but I guess this is not valid, so more rules should be specified.
If we need it to be about powers, then "I conjecture that every positive integer can be expressed uniquely by 127 binary digits"