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Gödel encoding expands your options considerably.


Primes are very common. So as long as you have a few bits to fiddle with in your file, you can probably make it a prime very quickly.

Given an arbitrary stopping point x, you have approximately x / log x primes between 1 and x.

In other words, for a file of length n, you have to try about O(n) slight variations to find a prime number.


A nice example are the drawings using prime numbers. For example see

"The Trinity Hall Prime - Numberphile" https://www.youtube.com/watch?v=fQQ8IiTWHhg

"The Emerging Art of Drawing in Prime Numbers" https://www.popularmechanics.com/science/math/a28649996/the-...




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