I take a known prime and prove it to be a composite (..or maybe need help?)

[Brian-E]

Originally Posted by storflyt32

Perhaps it is time for me to find something else to do instead?

No, not if you're still interested. Just don't use the forum as somewhere for your random jottings, which is what your postings amount to. Please read rajula's excellent advice again.

This forum is however a good place to ask questions about where you can learn more, or to get help if you don't understand something.

[CRGreathouse]

Originally Posted by storflyt32

Is the size of a given number a problem here?

I don't understand what you're trying to do in the first place, so I would say that -- rather than the size of the numbers -- is the problem.

[storflyt32]

Just in here to tell you that I found a PRP2036 before going to bed yesterday and was able to report it to the FDB.

Edit: Also a PRP938 just a couple of minutes ago. I am in the process of reporting it right now.

I am tempted to ask you the following question.

In some instances, numbers thought to be composite are in fact a product of large primes.

When it comes to the Mersenne numbers, both factoring and prime number finding by means of the LLR algorithm, these numbers are then called or nick-named Mersenne semiprimes.

A composite number like 1427247692705959880439315947500961989719490561 may be shown by means of proper factorization to be having the two prime factors 2305843009213693951 and 618970019642690137449562111.

These two factors, P19 = 2305843009213693951 and P27 = 618970019642690137449562111 corresponds to
(2^61)-1 and (2^89)-1 which are M9 and M10 (or Mersenne 9 and Mersenne 10), respectively.

These two factors are not that big in size. In the long run, they only become part of a larger picture in which there is a main separation or difference between prime numbers and composite numbers.

By means of doing such a thing, you will always want to know which numbers are composite and which numbers are prime. Also you would like to know in which way different numbers are linked together.

Definitely the process of factorization has its limits because of current technology. In the end we may become stuck with the general principle of multiplication and division when it comes to the handling of specific numbers.

[Jayder]

Please, if you want help, describe your objective in as few words and as coherently as you are able. I don't think anybody really knows what you are trying to do or say. You say you have a question to ask, but you never ask it. You also ask if you should move on to other things without making it clear what it is that you are doing. First: What are you trying to do? Second: What do you want help with?

In some instances, numbers thought to be composite are in fact a product of large primes.

These are still composite numbers. Semiprimes are still composite. But maybe you don't mean to suggest differently.

What are these PRPs and why are you searching for them?

The best that I can tell, you are asking if factoring and searching for primes is a worthwhile endeavor. That's up to you. The people here have made it into a hobby. If you're interested in it, pursue it. If you're not, forget about it, and count the money saved on your electricity bill. There are an infinite amount of numbers for which you will never know their full factorisations, let alone a single factor. Don't get hung up on it.

[ATH]

Originally Posted by storflyt32

When it comes to the Mersenne numbers, both factoring and prime number finding by means of the LLR algorithm, these numbers are then called or nick-named Mersenne semiprimes.

When Mersenne numbers are proven prime with the LL (Lucas-Lehmer) algorithm, they are called "Mersenne primes" not "Mersenne semiprimes". A semiprime is a composite number with just 2 prime factors.

[storflyt32]

Oops!

My bad.

Probably what I meant to say, though.

If you don't mind, writing it in full only wastes space.

If I just provide you with a syntax, you probably would not believe me.

As an example, try multiplying

(2^57131-1)/61481396117165983261035042726614288722959856631

with

(2^63703-1)/42808417

and then try factorizing this number next.

Probably it would not be working.

But both these numbers are prime numbers individually.

In the end they become just factors.

[Jayder]

I'm sorry, but you're not really saying anything revolutionary. Do you expect the factoring algorithms to magically and instantly know what numbers you happened to multiply together? That's not how that works. They don't instantly know what two primes you multiplied together any more than you know the precise date of my birth, or my mother's date of birth or my father's date of birth.

2 is a factor of 4. 2 is still a prime number. "Factor" does not mean "composite". Every prime number is a factor of an infinite amount of composite numbers. What are you trying to say? Please, provide us with a "syntax".

If you haven't done any reading on the subject, at least take a look at the first few chapters of
Hardy & Wright: Introduction to Number Theory (You can read this here: https://archive.org/details/AnIntrod...ardyE.m.Wright)

I like videos. Though I'm sure there are better videos on the topic out there, I quite like this channel: https://www.youtube.com/user/ArtOfTheProblem

[LaurV]

Originally Posted by storflyt32

But both these numbers are prime numbers individually.
In the end they become just factors.

I had at home two molecules of apple and one molecule of beer. After I ate them, they became just diarrhoea...
Welcome back kathegetes.
(Bots today become cleverer and cleverer!)

[Jayder]

Oh. Am I making a fool of myself, trying to talk to a bot or a troll? I was just about to give up.

[kladner]

Originally Posted by Jayder

Oh. Am I making a fool of myself, trying to talk to a bot or a troll? I was just about to give up.

I learned something from your efforts and explanations. I was also marveling at your patience and tolerance.

[Brian-E]

Originally Posted by Jayder

Oh. Am I making a fool of myself, trying to talk to a bot or a troll? I was just about to give up.

Like Kieren, I too admire your patience and tolerance. And it's always safest to assume someone is genuinely looking for help. Too often people are wrongly flagged as trolls when they are genuinely seeking help. But given the failure so far to take up or even acknowledge the help which you and various others have tried to give to the original poster in this thread, I think LaurV is right to nip this one in the bud now. But I might be wrong. It's always a very difficult call.