[LiveOverflow]

There is a database for prime factorisation: https://factordb.com/

And like the other people responded, there are just wayyyy to many primes to make that feasible. Though it is a common Challenge in security competitions to find the factors to a public key through factordb. Or having two bad keys sharing one same prime - then you can use Euclidean algorithm (greates common divisor).

[schoen]

> Or having two bad keys sharing one same prime - then you can use Euclidean algorithm (greates common divisor).

I wrote a puzzle in 2012 to help people understand this issue:

http://www.loyalty.org/~schoen/rsa/