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?