mersenneforum.org Please provide me really large numbers to test manually
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 2019-11-11, 15:21 #1 bosons   Nov 2019 112 Posts Please provide me really large numbers to test manually Please help me download really large numbers if they exist say trillion digits. I am a newbie in this forum
2019-11-11, 15:48   #2
R.D. Silverman

Nov 2003

164448 Posts

Quote:
If you do not know whether trillion digit numbers actually exist you need to learn some basic mathematics before you start discussing factoring methods.

I suggest you start by comparing the time needed to download such numbers against
the time it would take to generate them on your computer.

I also suggest that start your education process by googling for "factoring algorithms".
Read the material. I can suggest other references that you will need to study; A number
of books have been written about the subject. You will also need to read some books
on elementary number theory, as well as a book on multi-precision arithmetic, such as
Knuth's Art of Computer Programming.

2019-11-11, 15:57   #3
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

4,243 Posts

Quote:
What is it you're going to do to test a trillion digit number? Or billion digit? What test do you have in mind? How is this relevant to factoring (you posted in the factoring forum)?

2019-11-11, 16:42   #4
jwaltos

Apr 2012

337 Posts

Quote:
What makes you think such numbers may not exist?
What kind of computer "system" are you using and what is the mathematical software you are familiar with?

I had asked a similar question some time ago and it was suggested that rather than having a number provided I should use my noggin to find such numbers...large, unfactored Mersenne numbers were suggested and I'm suggesting those as well.

Last fiddled with by jwaltos on 2019-11-11 at 16:43

2019-11-11, 16:44   #5
bosons

Nov 2019

310 Posts

Quote:
 Originally Posted by VBCurtis What is it you're going to do to test a trillion digit number? Or billion digit? What test do you have in mind? How is this relevant to factoring (you posted in the factoring forum)?
I have developed a cool factoring algorithm over a period of 5 years. I had read Knuth while in School. I am 40 now.

I want to challenge myself to try to factor this monster on my laptop, if it exists. Till now I have success with RSA-32768.
Or you guys can challenge me with some decent examples and show me that my algorithm is not generic enough. I take this as a challenge for myself. I have never seen so large numbers. You guys are the experts when it comes to generating numbers.

But I have spent a decent period of 5+ years researching numbers. Thats all.

 2019-11-11, 17:10 #6 chris2be8     Sep 2009 34×23 Posts Try (14^214+1)/197 which evaluates to: Code: 948273052036079385652236848193016161726802429960072704995828354612138482026086831806250711003165469180610692471368787323762115176806614503658103635388433968893283088089524760828186888580799953409856008438896273930408368513447609232903906754061 That would take me about two weeks (using 4 reasonably fast systems). Chris
2019-11-11, 17:10   #7
R.D. Silverman

Nov 2003

164448 Posts

Quote:
 Originally Posted by bosons I have developed a cool factoring algorithm over a period of 5 years. I had read Knuth while in School. I am 40 now. I want to challenge myself to try to factor this monster on my laptop, if it exists. Till now I have success with RSA-32768. Or you guys can challenge me with some decent examples and show me that my algorithm is not generic enough. I take this as a challenge for myself. I have never seen so large numbers. You guys are the experts when it comes to generating numbers. But I have spent a decent period of 5+ years researching numbers. Thats all.
Turn on the crankometer. This last post piles on the points.

Last fiddled with by R.D. Silverman on 2019-11-11 at 17:17 Reason: small addition

2019-11-11, 17:29   #8
Dylan14

"Dylan"
Mar 2017

499 Posts

Quote:
 Originally Posted by bosons I want to challenge myself to try to factor this monster on my laptop, if it exists. Till now I have success with RSA-32768.
If you actually managed to factor RSA-32768 in reasonable time on your laptop then you have basically rendered the algorithm that we use for public key cryptography obsolete. I’d like to see the proof of this.
But as for numbers, here’s a couple to try:
home prime base 10, start value 49, index 119
Code:
 26633090926792263436736904630531520479768742849435097127754634822168395438250791486509180275478812779959346908131589660697709489852830934711978704681639399323263270697821325581691729538877317736626598036703631970679737664887720652086830617767029002763
(and if that’s easy, compute the rest of the sequence)
Phi_{18000000000}(10) (needed for a OEIS sequence)
EM(52) (definition here: https://en.wikipedia.org/wiki/Euclid–Mullin_sequence)

2019-11-11, 18:05   #9
bosons

Nov 2019

112 Posts

Quote:
 Originally Posted by Dylan14 If you actually managed to factor RSA-32768 in reasonable time on your laptop then you have basically rendered the algorithm that we use for public key cryptography obsolete. I’d like to see the proof of this. But as for numbers, here’s a couple to try: home prime base 10, start value 49, index 119 Code:  26633090926792263436736904630531520479768742849435097127754634822168395438250791486509180275478812779959346908131589660697709489852830934711978704681639399323263270697821325581691729538877317736626598036703631970679737664887720652086830617767029002763 (and if that’s easy, compute the rest of the sequence) Phi_{18000000000}(10) (needed for a OEIS sequence) EM(52) (definition here: https://en.wikipedia.org/wiki/Euclid–Mullin_sequence)

Thank you everybody in the forum who helped me with those examples to try out. When you say reasonable time, its actually sub second range, below a second. Cranking out a paper for Nature.com journal to get that credit. I will try out the examples right away . My laptop has 8GB RAM. At one point I am taking the log of the number to be factored. So trillion digits would anyways not fit by conventional methods. And I dont know how to manipulate numbers on disk by simple methods. I could write a algorithm myself but I know its a chore.

2019-11-11, 18:13   #10
xilman
Bamboozled!

May 2003
Down not across

10,193 Posts

Quote:
 Originally Posted by bosons Thank you everybody in the forum who helped me with those examples to try out. When you say reasonable time, its actually sub second range, below a second. Cranking out a paper for Nature.com journal to get that credit. I will try out the examples right away . My laptop has 8GB RAM. At one point I am taking the log of the number to be factored. So trillion digits would anyways not fit by conventional methods. And I dont know how to manipulate numbers on disk by simple methods. I could write a algorithm myself but I know its a chore.
8-(

2019-11-11, 18:15   #11
storm5510
Random Account

Aug 2009
U.S.A.

101010010002 Posts

Quote:
As a newbie, you must learn to respect the people here! Earning their respect may take quite a while. Using the cattle-prod approach will get you nowhere, rapidly.

As for your idea, I must ask why? Take a look at the Work Distribution Map on https://www.mersenne.org. There is probably decades of work which needs to be done there.. Another project, ran by James Heinrich, goes beyond. This can be seen at https://www.mersenne.ca.

What I am suggesting is to do the work which can be completed with the current technology and software available now, and nothing more. As for the rest, it will come along in time.

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