[necovek]

> If I publish a paper saying I have an algorithm which can factor large composites, and in the paper publish the factors to all of the RSA numbers

If some factors of those numbers are also large composites, without access to a good algorithm, nobody can truly verify your claims.

If not and you include all of those factors in an easily digestible way for computers to process (let's call that "code"), it will be easy for anyone to reproduce your results (run that code which multiplies all the factors and gets the resulting RSA numbers).

With code, they could easily check that there's not an error in your verification method too (eg. large number multiplication broken).

This would achieve both goals: you'd withhold your algorithm for security reasons, and your results would be easier to verify.

Edit: but to be honest, I think withholding the research is a bit of a special case. You are doing it on purpose, and you can easily offer a service to prove your algorithm works (eg. imagine a "factoring" web service that instantly gives you a hash of the resulting sequence of factors, and then only mails you the actual sequence in two days).

[aliceryhl]

It's a lot easier to check if something is a prime than to factor it.