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-   -   Endomorphisms and Factoring (https://www.mersenneforum.org/showthread.php?t=22424)

manasi 2017-06-28 22:47

Endomorphisms and Factoring
 
1. I need to find out a program that only deals in machine level 0s and 1s. What I mean is unlike C++, Java, etc...decimals are not converted to binary but it is a program where every number dealing is binary. There should be no fixed integer range so large blocks can be dealt with in a good way.

2. So, the supposed mersenne prime to binary. The about to be tested primes(P) are also in binary.

Then, one uses endomorphisms [f][/P] which makes all the P appearances in the block supposed Mersenne prime to 000 s of P length. Then another endomorphism just performs subtraction right from the first or second place below 1's in the block. This can be created as a function.

I am just looking for a program that handles large binary numbers. I am also open to knowing more about endomorphisms and factoring if there exists such theory.

chalsall 2017-06-28 22:54

Just putting this out there for consideration...

Do any other regular Mersenne Forum members find it a bit odd that there are many new participants who get the "lingo", but ask really stupid questions?

science_man_88 2017-06-28 23:03

[QUOTE=chalsall;462317]Just putting this out there for consideration...

Do any other regular Mersenne Forum members find it a bit odd that there are many new participants who get the "lingo", but ask really stupid questions?[/QUOTE]

Could be my fault, I think I once posted a link to the forum, on a youtube comment, on a numberphile video.

paulunderwood 2017-06-28 23:04

[QUOTE=manasi;462316]1. I need to find out a program that only deals in machine level 0s and 1s. What I mean is unlike C++, Java, etc...decimals are not converted to binary but it is a program where every number dealing is binary.
[/QUOTE]

[URL="http://pari.math.u-bordeaux.fr/"]Pari/GP[/URL] has a function called binary(). For example:

[CODE]? n=2^17-1;
? binary(n)
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[/CODE]

manasi 2017-06-28 23:05

That is a rude message. Is it not? If my question is that trivial to you, then you could have done the honours of answering it. Did you get my post?

manasi 2017-06-28 23:08

Thank You. I will check out PARI/GP.

science_man_88 2017-06-28 23:36

[QUOTE=manasi;462321]Thank You. I will check out PARI/GP.[/QUOTE]

[url]https://en.wikipedia.org/wiki/Machine_code[/url] might also be something to read.

manasi 2017-06-28 23:48

@science man: That is not what I am saying, people use high level language. It converts everything to machine code. My problem is with HLLs and their fixd integer range which makes prime factoring or mathematical computations difficult. So I am looking for a modern low level program where the number system is binary and like machine language , since large amounts of bits and bytes are stored, working with them is simple. Prime factoring would be very comfortable with elementary computations.

chalsall 2017-06-28 23:50

[QUOTE=manasi;462320]That is a rude message. Is it not? If my question is that trivial to you, then you could have done the honours of answering it. Did you get my post?[/QUOTE]

A very wise man once told me that I didn't need to bat at every ball.

He also wisely told me that sometimes you simply touch the ball to cause a little trouble, when it was worth the effort.

RIP ROK.

paulunderwood 2017-06-28 23:55

[QUOTE=manasi;462325]@science man: That is not what I am saying, people use high level language. It converts everything to machine code. My problem is with HLLs and their fixd integer range which makes prime factoring or mathematical computations difficult. So I am looking for a modern low level program where the number system is binary and like machine language , since large amounts of bits and bytes are stored, working with them is simple. Prime factoring would be very comfortable with elementary computations.[/QUOTE]

If you have linux you could use the [URL="https://en.wikipedia.org/wiki/Bc_%28programming_language%29"]bc language[/URL]:

[CODE]bc 1.06.95
Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'.
ibase=2
obase=2
101010*101001
11010111010
[/CODE]

I think you can get it for Windows and iPhone :smile:

Dubslow 2017-06-29 00:01

[QUOTE=manasi;462325]@science man: That is not what I am saying, people use high level language. It converts everything to machine code. My problem is with HLLs and their fixd integer range which makes prime factoring or mathematical computations difficult. So I am looking for a modern low level program where the number system is binary and like machine language , since large amounts of bits and bytes are stored, working with them is simple. Prime factoring would be very comfortable with elementary computations.[/QUOTE]

Do you mean something like GMP?

Yes, every language still fundamentally works in binary, but typically in fixed-width binary. GMP is a library for C (and therefore all its derivatives) that allows for arbitrary-size integers. It's very common in big number prime testing and factorization code.

[url]https://en.wikipedia.org/wiki/List_of_arbitrary-precision_arithmetic_software[/url]

A lot of the languages and software packages in the above list use GMP under the hood.


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