Which programming language is recommended in number theory?

[mersenne1588]

I am interested in various topics in number theory (Mersenne Prime Search, Goldbach's conjecture, Collatz conjecture, odd perfect numbers, etc ...).

If I would like to carry out tests myself according to my ideas in this context and if I would like to learn therefor a corresponding programming language, which programming language can you recommend? C ++?

[xilman]

Originally Posted by mersenne1588

I am interested in various topics in number theory (Mersenne Prime Search, Goldbach's conjecture, Collatz conjecture, odd perfect numbers, etc ...).

If I would like to carry out tests myself according to my ideas in this context and if I would like to learn therefor a corresponding programming language, which programming language can you recommend? C ++?

I would recommend learning number theory.

You will make more progress more rapidly than writing code in any given programming language.

[mersenne1588]

Originally Posted by xilman

I would recommend learning number theory.

You will make more progress more rapidly than writing code in any given programming language.

I already have some experience in number theory. I just want to know if I want to carry out various tests and program them myself, which programming language is recommended here? C ++?

[paulunderwood]

Pari/GP is both expressive and good for prototyping. For speed C plus GMP, even assembly.

[BudgieJane]

Originally Posted by mersenne1588

I already have some experience in number theory. I just want to know if I want to carry out various tests and program them myself, which programming language is recommended here? C ++?

Do you have any programming experience already? If the answer to that is "no" then you do not want to learn a programming language such as C++, because you will spend all your time fiddling with trivial programming details trying to get your programs right, and none of your time doing your number theory research. I suggest you follow Paul Underwood's advice and look at Pari/GP, which is a prewritten package designed for the sort of use you are looking for.

[Batalov]

Originally Posted by paulunderwood

Pari/GP is both expressive and good for prototyping. For speed C plus GMP, even assembly.

Pari/GP - Seconded/thirded! Great for prototyping in one-two lines, and for learning.

Same for speed, plus to C plus GMP... you can link to GWNUM for many good things. Just need to learn the APIs. You can also borrow from the masters - you take the well-respected tool, understand its source, and code about your problem using that envelope and all facilities that come with it, and recompile. This approach requires less coding but much more reading and thinking. But you will be learning from the masters.

[Billtorntn]

I can recommend you Python, however, its implementation can be slow. Also, you may consider C++ and Java if you aren't afraid of lots of syntax.
PARI/GP is C-based as well. So I upvote the previously mentioned replies too.

[CRGreathouse]

PARI/GP is good, and since PARI is a C library it transitions well into that language for higher-performance computing when needed (you can use gp2c if you want to live in both worlds).

[drkirkby]

Sagemath https://www.sagemath.org/ is particularly strong on number theory. It includes Pari/GP. I spent many man months working on porting Sage, as it was called then, to Solaris. My mathematical input is zero.

It seems a bit pointless to me trying to learn C++ to do number theory. Two quite different skills, and no need to mix the two.