![turing programming language list first n primes turing programming language list first n primes](https://gaurish4math.files.wordpress.com/2017/07/mat.png)
- #TURING PROGRAMMING LANGUAGE LIST FIRST N PRIMES PATCH#
- #TURING PROGRAMMING LANGUAGE LIST FIRST N PRIMES SERIES#
If that results in 0, pop the 0 and discard it.ħ (16): Duplicate the top integer on the stack.Ĩ (25): Halt execution and print the stack contents. If it was 1, increment the top integer on the stack.Ħ (15): Decrement the top integer on the stack.
![turing programming language list first n primes turing programming language list first n primes](https://i1.rgstatic.net/publication/24167007_Complexity_of_Fractran_and_Productivity/links/5419b3480cf2218008bf9c7e/largepreview.png)
In detail, the commands are:Ģ (smallest integer producing this command: 1): Push the next integer in the program onto the stack.ģ (smallest producing integer: 4): Pop the top integer on the stack and execute the command associated with it.Ĥ (smallest: 6): Pop the top integer. If the stack ever holds 0, the 0 is immediately removed. The language's commands modify a stack, which can hold arbitrarily large positive integers. Which command it is assigned to is based on the number of primes between its square and the next integer (equivalent to the OEIS sequence A014085). Each integer corresponds to a base command in Legendre, or a potential user-defined one.
#TURING PROGRAMMING LANGUAGE LIST FIRST N PRIMES SERIES#
Programs in Legendre are made up of series of positive integers (0 is especially banned, because it essentially negates the entire purpose of the language). This language takes some inspiration from Underload, though in some respects it is very different from it. there exists a integer n > 0 such that there are no primes between n^2 and (n+1)^2. This language is only Turing-complete if and only if Legendre's conjecture is false, i.e. It should be interesting as a standalone esoteric language. I prefer to make my esolangs' gimmicks more firmly baked into the language Changing an existing language to fit the specifications is fine but patching on a condition is discouraged because it is boring.
#TURING PROGRAMMING LANGUAGE LIST FIRST N PRIMES PATCH#
It should not be a simple patch of an existing language. What should a good answer do? Here are some things to look for when voting but are not technically required This is a popularity-contest so the answer with the most votes will win. Since we are concerned with Turing Completeness I/O is not required, however the goal is to make the most interesting language so it might help. You may assume access to unbounded memory when running the interpreter or compiled program. You must include a proof as to why it would be Turing complete or incomplete based on the chosen conjecture. (or if and only if the conjecture doesn't hold) The programming language must be Turing complete if and only if the conjecture holds. You must provide a specification of the language and an implementation in an existing language.
![turing programming language list first n primes turing programming language list first n primes](https://assets.cambridge.org/97811087/92745/large_cover/9781108792745i.jpg)
It can be any provable conjecture in mathematics not just one of the ones listed on the Wikipedia page. The problem you choose must have be posed at least 10 years ago and must be unsolved, as of the posting of this question. Your task is to devise and implement a language whose Turing Completeness relies on a major unsolved problem in Mathematics. Lets make some programming languages that are so hard to prove Turing Complete that even the best mathematicians in the world will fail to prove them either way. It is a also a pretty difficult task for a lot of esoteric programming languages to begin with, but lets kick it up a notch. Determining whether a Language is Turing Complete is very important when designing a language.