20210131, 11:58  #1 
Feb 2019
2^{2}×7 Posts 
Which programming language is recommended in number theory?
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 ++? 
20210131, 13:22  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
10110100111001_{2} Posts 
Quote:
You will make more progress more rapidly than writing code in any given programming language. 

20210131, 14:04  #3 
Feb 2019
2^{2}×7 Posts 
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 ++?

20210131, 14:19  #4 
Sep 2002
Database er0rr
3×1,453 Posts 
Pari/GP is both expressive and good for prototyping. For speed C plus GMP, even assembly.

20210205, 21:24  #5 
"Jane Sullivan"
Jan 2011
Beckenham, UK
2×3×53 Posts 
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.
Last fiddled with by BudgieJane on 20210206 at 17:44 Reason: typo 
20210205, 21:56  #6  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23403_{8} Posts 
Quote:
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 wellrespected 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. 

20210223, 19:31  #7 
Jan 2021
2 Posts 
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 Cbased as well. So I upvote the previously mentioned replies too. 
20210224, 05:17  #8 
Aug 2006
5,987 Posts 
PARI/GP is good, and since PARI is a C library it transitions well into that language for higherperformance computing when needed (you can use gp2c if you want to live in both worlds).

20210314, 18:27  #9 
"David Kirkby"
Jan 2021
Althorne, Essex, UK
701_{8} Posts 
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. Last fiddled with by Uncwilly on 20210314 at 18:42 Reason: Removed fluff 
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