Endomorphisms and Factoring

[Dubslow]

Originally Posted by manasi

Well, the only problem is there is a certain integer range that is acceptable as space for an integer(signed or unsigned int). There is a problem if you have to check a number like 2^10000019 -1 is prime or not. Most programs can not handle operations with large numbers.

That's precisely why I suggested GMP. Instead of writing [c]a = a + b*c[c], which is limited by the machine word size as you say, but with GMP you write, in C or any other language GMP supports, you write mpz_addmul(a, b, c) which works for numbers a, b, c of arbitrary size, hundreds of digits, thousands of digits, etc.

Frankly, the things you say seem to indicate you know very little about how computers actually work, and your talk about "endomorphisms" is equally meaningless from a mathematical perspective. You have no idea what you're doing, which is why you got such a snarky response to your initial post.

[manasi]

Originally Posted by Dubslow

That's precisely why I suggested GMP. Instead of writing [c]a = a + b*c[c], which is limited by the machine word size as you say, but with GMP you write, in C or any other language GMP supports, you write mpz_addmul(a, b, c) which works for numbers a, b, c of arbitrary size, hundreds of digits, thousands of digits, etc.

Frankly, the things you say seem to indicate you know very little about how computers actually work, and your talk about "endomorphisms" is equally meaningless from a mathematical perspective. You have no idea what you're doing, which is why you got such a snarky response to your initial post.

Well, I know less about - GMP if you mean to say GMP has no restriction on space. I have been talking about working with very large numbers. I do know that decimal numbers are stored in binary or any data for that matter.

But what is the problem with f: [Z][/2] -> [Z][/2].
Well, I have been using homomorphisms(under * or +) on binary numbers. What is the problem with math? It is clear and very simple, is it not? Besides, this is an Algebra thread.

[CRGreathouse]

Originally Posted by manasi

No idea if I can go faster. Didn't exactly write and compare the two algorithms. Just wanted to try different.

I don't mean that you shouldn't try, but that I don't see anything different. As far as I can tell your suggestion is to use binary, but everyone is using binary.

[CRGreathouse]

Originally Posted by manasi

Well, I know less about - GMP if you mean to say GMP has no restriction on space. I have been talking about working with very large numbers.

There are a number of different limitations to consider.

First are architectural limitations. I'm not sure what it is for GMP but for example in PARI/GP you can have t_REAL numbers up to almost 2^2^29 on 32-bit systems and 2^2^61 on 64-bit systems.

Next there are memory limitations. If you want to store 2^10^15 directly you need 10^15 bits of memory. On 64-bit systems this is more likely to cause trouble than architectural limitations.

Finally there are practical limitations imposed by the algorithms used. If you want to factor the numbers, it doesn't matter if you could store billions of digits because you won't live long enough for a current computer running current software to factor such a beast.

[ET_]

If the OP refers to Frobenius endomorphism of GF(N^2), this method is not deterministic. This was established by Grantham.
They are nothing more than PRP tests. And, owing to the work of Pomerance and Kim, they are not even as useful as a MR test. For the latter we have good estimates of the probability that the result of a test is in error. However, the Pomerance/Kim analysis will not work for your tests.

[LaurV]

@OP:

1. Click on "Start" button
2. Click on "All programs"
3. Click on "Accessories"
4. Click on "Calculator"
5. Click on "View" and select "Programmer"
6. Click on "Bin" radio button.
7. Voila! Enjoy!

For how you talk, you seem not to be needing more... The only problem is that you may need to launch the magnifier program too (also in accessories) because as the binary number grows bigger, the digits become smaller, due to the limited space and non-sizeable window.. A real magnifier glass may do wonders... It can also be from plastic, it doesn't matter.



Edit: tip: you can modify the numbers directly clicking on the powers of two on the gray area, you do not need to input all numbers bit by bit...