MHB Factorisation Related Question

  • Thread starter Thread starter PeterJ1
  • Start date Start date
AI Thread Summary
Factoring large numbers, such as a 1050-digit number, poses significant computational challenges, particularly with traditional methods. The discussion highlights that multiplying primes sequentially may be computationally easier than direct factorization. A reference to the time taken to factor a 232-digit number illustrates the increasing difficulty with larger digits. The consensus is that as numbers grow, factorization becomes increasingly problematic for current algorithms. The initial question about the comparative ease of the two calculations remains central to the discussion.
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.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

MHB Few more questions from 6th Grade text onward ,Please help ?
Replies
2
Views
2K
Proof of PSF quadratic factorising
Replies
1
Views
4K
I Questions regarding Kurepa's Conjecture
Replies
1
Views
2K
I Karatsuba multiplication implementation question
Replies
3
Views
2K
MHB Sum of 2 Primes: 45 - (2 Digit Integer)?
Replies
4
Views
2K
I Is this a proof of the Collatz Conjecture?
Replies
8
Views
3K
I What is the probability that the product of the digits is odd?
Replies
13
Views
2K
MHB Problem of Calculating Probabilities
Replies
2
Views
2K
MHB Powers function n^5+n^4=(n^5−n^3)(n−1)−(n−2)
Replies
5
Views
3K
MHB Appending a number to itself n times and finding modulo m
Replies
6
Views
3K

Hot Threads

Recent Insights

Back
Top