Factorisation Related Question

  • Context: MHB 
  • Thread starter Thread starter PeterJ1
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the challenges of factoring large numbers, specifically a number with 1050 digits, and compares two methods of calculation: direct factorization and sequential multiplication of primes. Participants explore computational difficulties associated with these methods and the implications for current factorization techniques.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether calculating the product of primes sequentially would be significantly easier than directly factorizing a large number.
  • Another participant references the time taken to factor a 232-digit number, suggesting that larger numbers would require exponentially more time, but does not directly address the computational ease of the two methods.
  • A later reply indicates that the participant has realized the answer to their second question is obvious, implying a shift in understanding but does not elaborate on the reasoning.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the computational ease of the two methods or the specific digit threshold at which factorization becomes problematic.

Contextual Notes

Participants reference specific examples and estimates related to factorization times but do not provide a clear threshold for when factorization becomes a significant problem. The discussion lacks detailed exploration of the assumptions behind the computational methods mentioned.

PeterJ1
Messages
17
Reaction score
0
A slightly odd layman's question about factoring large numbers and comparing two calculations.

Call N a number with 1050 digits.

1) Factorise N
2) Multiply the primes sequentially from 2 onwards until the product is as close as possible to N.

Would calculation 2 be significantly easier computationally than calculation 1?

How many digits would a number has to have before factorisation becomes a problem for our current methods?

Thanks
 
Mathematics news on Phys.org
Thanks Greg.

"... to factor a 232-digit number (RSA-768) utilizing hundreds of machines took two years and the researchers estimated that a 1024-bit RSA modulus would take about a thousand times as long.[1]"

This helps with the second question but not the first, which is my main question.
 
Doh! On reflection the answer to the second question is obvious. Consider it answered.
 

Similar threads

MHB Few more questions from 6th Grade text onward ,Please help ?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Proof of PSF quadratic factorising
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Questions regarding Kurepa's Conjecture
  • · Replies 1 ·
Replies
1
Views
2K
MHB Sum of 2 Primes: 45 - (2 Digit Integer)?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Karatsuba multiplication implementation question
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Is this a proof of the Collatz Conjecture?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad What is the probability that the product of the digits is odd?
  • · Replies 13 ·
Replies
13
Views
3K
MHB Powers function n^5+n^4=(n^5−n^3)(n−1)−(n−2)
  • · Replies 5 ·
Replies
5
Views
3K
MHB What is the last odd digit in the factorial sequence?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Equivalent Goldbach proof impossible question.
  • · Replies 2 ·
Replies
2
Views
2K