Didn't even find a useless factor of an uninteresting number! Take that!

[cuBerBruce]

I think you should read a book about basic number theory. I suggest the book A First Course in Number Theory by Hugh M. Edgar. You can get it through Amazon.com for $2,629.01 + $3.99 shipping.

[storflyt32]

Became a little long.

Thanks for the tip, by the way. Did not notice after posting.

But found another good example.


http://factordb.com/index.php?id=1100000000805440883

http://factordb.com/index.php?id=1100000000805440839


The P40 and P50 in the first link is a better one.

Not me this time. Thanks to the one who did that job.

But the second link apparently is a quite difficult one.

Here I do not have the bit length or the similar, but possibly this number could be as difficult as a RSA-512.

The evident fact is that even though the factors may be found for this number, you already know that they will not be factors of RSA-1024.

If 35 for some reason is the big composite number you would like to factorize, you already know that some number in between which is composite, like 12 or 18, may not be having factors of 35.

Even prime factors, like 3, 11, 13, 17, or 19 will not be the same when it comes to being so.

Easy to say when the numbers are small, but when they grow in size, the numbers in between become many more.

Therefore, rather than asking the question about the possible factors of a given number, like RSA-1024, it may better be asked a couple of questions about the way specific factors are being determined in a similar way.

RSA-512 apparently became factored by means of the usual factorization.

RSA-768 is supposed to have been factored in the same way.

Therefore, if a number is not supposed to be readily factorized, in which way are you supposed to be able to determine the exact or precise factors for a number where such a factorization is supposed to be possible?

Right now there apparently is no clear answer to this question.

[Batalov]

Have you heard of a Good Soldier Schweik? It is a fictional character created by a Czech writer Jaroslav Hasek in 1914 but still popular all around the world.

At some point in the book Schweik demonstrates such enthusiasm in serving the Emperor that his sanity is questioned and he appears before the medical board. He is asked by the certified psychologists:

"Is radium heavier than lead?"
"Please sir, I haven't weighed it," answered Schweik with his sweet smile.
"Do you believe in the end of the world?"
"I'd have to see that end first," Schweik answered nonchalantly. "But certainly I shan't see it tomorrow."
"Would you know how to calculate the diameter of the globe?"
"No, I'm afraid I wouldn't," answered Schweik, "but I'd like to ask you a riddle myself, gentlemen. Take a three-storied house, with eight windows on each floor. On the roof there are two dormer windows and two chimneys. On every floor there are two tenants. And now, tell me, gentlemen, in what year the valet's grandmother died?"

...And now, tell us, storflyt32, in what year the valet's grandmother died?

Most of your circular arguments go around something that seems to be visible only to you through your magic glasses.

"This is a factor of this, and that is a factor of that, and I don't even know the factors of that third one... so now we finally know that they will not be factors of RSA-1024." WTF? Why? "If 35 for some reason is the big composite number you would like to factorize, you already know ... bla-bla-bla... " -- what do we already know then? That 35 = 5 * 7 and now we finally know that 5 or 7 will never divide anything else in the world?? They've been "spent"? They've been so tired from dividing 35 that they will never divide anything else? Or what is it?

[science_man_88]

I think storflyt32 is basically saying that like fermat factors and mersenne factors ( which apparently aren't supposed to mingle something I didn't know) the factors of RSA number may not mix and so we can eliminate the factors of one form factors of the other ?

[storflyt32]

http://factordb.com/index.php?id=1100000000805495792

Here you may find an example where different types of numbers are relating to each other.

[retina]

Originally Posted by storflyt32

... may not be having ...

From India? I've encountered that English formation a lot in India. I be having memories of being in India now.

[storflyt32]

http://factordb.com/index.php?id=1100000000805512949

http://factordb.com/index.php?id=1100000000805512928


The initial C131 in the first link.

Should I perhaps factorize this number before reporting the factors?

Or perhaps I already did so.

[Batalov]

Originally Posted by storflyt32

http://factordb.com/index.php?id=1100000000805512949

http://factordb.com/index.php?id=1100000000805512928


The initial C131 in the first link.

Should I perhaps factorize this number before reporting the factors?

Or perhaps I already did so.

[MOD HAT ON /] Fair warning: Post another couple of useless factordb.com links and you will be banned for spamming.
[OFF /]

[storflyt32]

Psst, or hush.

Should perhaps not be telling, but here I just came across two factors which are having only
P1 = 2 and P1 = 7 in between before dividing RSA-2048.

Both ways, that is.

I will not be mentioning the factors here, but suffice to say that they are a P296 and a P320, respectively.

Multiplying the two factors and it becomes a C616 as a result,

Still have to multiply by 14 in order to catch up with the desired number.

At least when dividing, I get 14 back in return, which is 2 * 7.

This result ends up in my notes.

[storflyt32]

So perhaps a fair or honest question about something else, since I was lucky this time.

Right now the Mersenne primes are the largest known prime numbers.

Their syntax are ending with -1.

So, for some other numbers related to prime number finding, including the PrimeGrid 321 Search, The Riesel Problem and Woodall Prime Search, the same syntax is being common, although 321 also is dealing with +1 in its syntax.

Is it possible to make a correspondence or relationship between the sizes of the prime numbers that could be found for such projects when comparing just the different syntaxes for these numbers?

You may be able to find a megaprime by means of running either a 321 LLR or a Riesel LLR task, but these numbers may not be able to beat any Mersenne prime when it comes to its size.

Definitely all these projects are dealing with numbers that are being computed respective to their ranges.

A specific number for k, b or p, or the similar determines the exact size of the whole number, or possibly its composition.

The number for n is determining the total size of the whole number. Multiplying for example k with n and next adding or subtracting 1 could possibly determine whether or not such a number is prime.

Any answers are welcome.

[science_man_88]

Originally Posted by storflyt32

Is it possible to make a correspondence or relationship between the sizes of the prime numbers that could be found for such projects when comparing just the different syntaxes for these numbers?

I think the problem is that some algorithms don't even need to know of a factor ( mersenne numbers have the LL test to tell if they are composite for example only relying on the exponent for the number of iterations.) so syntax of the number itself is only needed to weed things out. if you look at the mersenne factor candidate form 2kp+1 you can form any odd number greater than or equal to 5 so in theory you could find any size prime by trial factoring a mersenne number without limits in theory. so other than the time it takes there's probably no ratio you'll find that stays still ( I may be wrong).