20191111, 15:21  #1 
Nov 2019
11_{2} 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 
20191111, 15:48  #2  
Nov 2003
16444_{8} Posts 
Quote:
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 multiprecision arithmetic, such as Knuth's Art of Computer Programming. 

20191111, 15:57  #3 
"Curtis"
Feb 2005
Riverside, CA
4,243 Posts 
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)?

20191111, 16:42  #4  
Apr 2012
337 Posts 
Quote:
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 20191111 at 16:43 

20191111, 16:44  #5  
Nov 2019
3_{10} Posts 
Quote:
I want to challenge myself to try to factor this monster on my laptop, if it exists. Till now I have success with RSA32768. 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. 

20191111, 17:10  #6 
Sep 2009
3^{4}×23 Posts 
Try (14^214+1)/197 which evaluates to:
Code:
948273052036079385652236848193016161726802429960072704995828354612138482026086831806250711003165469180610692471368787323762115176806614503658103635388433968893283088089524760828186888580799953409856008438896273930408368513447609232903906754061 Chris 
20191111, 17:10  #7  
Nov 2003
16444_{8} Posts 
Quote:
Last fiddled with by R.D. Silverman on 20191111 at 17:17 Reason: small addition 

20191111, 17:29  #8  
"Dylan"
Mar 2017
499 Posts 
Quote:
But as for numbers, here’s a couple to try: home prime base 10, start value 49, index 119 Code:
26633090926792263436736904630531520479768742849435097127754634822168395438250791486509180275478812779959346908131589660697709489852830934711978704681639399323263270697821325581691729538877317736626598036703631970679737664887720652086830617767029002763 Phi_{18000000000}(10) (needed for a OEIS sequence) EM(52) (definition here: https://en.wikipedia.org/wiki/Euclid–Mullin_sequence) 

20191111, 18:05  #9  
Nov 2019
11_{2} Posts 
Quote:
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. 

20191111, 18:13  #10  
Bamboozled!
May 2003
Down not across
10,193 Posts 
Quote:


20191111, 18:15  #11  
Random Account
Aug 2009
U.S.A.
10101001000_{2} Posts 
Quote:
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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