MHB Factorisation Related Question

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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.
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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
 
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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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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