20110122, 00:21  #1 
May 2004
New York City
2^{3}×23^{2} Posts 
Yet another basicfactoringquestions thread
Perhaps you could transfer him some of yours.

20110122, 18:39  #2  
May 2004
New York City
4232_{10} Posts 
Quote:
What do b1 and B1 bounds refer to in their respective P1 and P+1 factoring programs? How sure is pretty sure? Who if anyone can manage a C210 at this point? Could anyone manage a C1000 right now? You don't have to give away anything you don't want to. 

20110122, 19:01  #3  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Yet another basicfactoringquestions thread
Quote:
Quote:
No. At least, not to definitely be able to factor it, as in factoring with SNFS or GNFS. It is possible for people to look for small factors of a C1000 or larger, and in some cases these might completely factor the number, but that's not the same. You can see the records for integer factorization here, the largest done yet for general and special forms are 232 and 313 digits, respectively. Last fiddled with by MiniGeek on 20110122 at 19:04 

20110122, 19:13  #4  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10100101011011_{2} Posts 
Quote:
B1 in P1, P+1 and ECM indicated that every prime power e <= B1 has been included in the computation of a^x where x = Product e. a is the initial value and arithmetic is performed in the appropriate ring. I estimate that the probability pf finding a factor under 40 digits is below 1%, given the amount of computation already performed. I can't give a more precise estimate because I don't know how much work has been done. Factoring a general 210digit composite could be done by at most a few (<5) teams known to be currently active in the field. Finding out who those people are is left as a simple exercise in the use of Google or the search engine of your choice. State of the art is <250 digits for a general composite. 1000 digits is likely to be inaccessible for a very long time unless there is a major breakthrough in theory. I have a bet open with RDS that 310 digits will be achievable before 2020. Even if I win the bet, I doubt I will collect much more than 2 years ahead of the deadline. Paul Last fiddled with by xilman on 20110122 at 19:15 

20110122, 19:16  #5  
May 2004
New York City
2^{3}·23^{2} Posts 
Quote:
Is SNFS the Special Number Factor Sieve? Is GNFS the General Number Factor Sieve? What's special about those special numbers? Are they a^b +/ c ? What's general about those general numbers? (I know there's a long answer to that question, but I'd be glad for a good short one). That's all I've got for now ..... 

20110122, 19:22  #6  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4267_{10} Posts 
Quote:
http://www.mersenneforum.org/showthr...734#post247734 Last fiddled with by MiniGeek on 20110122 at 19:22 

20110122, 19:27  #7  
May 2004
New York City
2^{3}·23^{2} Posts 
Quote:
let me computify: if I were given a large number in terms of its digits, say what appears to be a 400digit random decimal number, my first attempt would be check the units digit for 0 or 2 or 4 or 6 or 8 or 5. Then I would quickly check onedigit 3 and 7 to get 10smooth. Then because I'm not a computer and long division takes a bit longer, I'd write an arbitrary precision integer decimal calculator to handle the big number arithmetic (using Knuth), which I did a few years ago. So I'd let it divide by the small primes. My last version went as high as 10 billion, but of course slows down when the highest TF factors exceed 2^32. Not being familiar with ECM yet, I'd then turn to Mersenne forum for the next suggested step in factoring Y400 (the given number). What next? 

20110122, 19:28  #8  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3×3,529 Posts 
Quote:
Numbers of the form a^b+/c, where a, b and c are all small, are just a special case of special numbers. They can (resp .can not) be represented by a polynomial with "small" coefficients. This last point is rather subtle and you should read up on the Number Field Sieve for what that statement actually means. Paul 

20110122, 19:32  #9  
May 2004
New York City
2^{3}×23^{2} Posts 
Quote:
to get info on Number Field Sieve (NFS)? No simple link right here from this thread to keep things simple and organized? 

20110122, 20:29  #10  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
24533_{8} Posts 
Quote:
Paul Last fiddled with by xilman on 20110122 at 20:30 

20110122, 20:31  #11 
May 2004
New York City
2^{3}·23^{2} Posts 

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