MHB Factorisation Related Question

[PeterJ1]

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

 

[Greg]

https://en.wikipedia.org/wiki/Integer_factorization

 

[PeterJ1]

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.

 

[PeterJ1]

Doh! On reflection the answer to the second question is obvious. Consider it answered.