[schoen]

It might not be a good idea for other reasons to have them on your screen, where other locally-installed software could view them, they would be (more strongly) broadcast in the RF spectrum, someone might see them over your shoulder, etc.

[userbinator]

Valid points about other software, but I don't think 1000+-digit random-looking numbers would be easily memorised by someone looking over your shoulder casually.

http://www.recordholders.org/en/list/memory.html#numbers-1mi...

[schoen]

If you had a 2048-bit public key modulus, each factor (only one factor is sufficient to reconstruct the private key) is only about 308 decimal digits, or 256 hex digits. :-)

We also know from Nadia Heninger and Hovav Shacham's research that you can reconstruct private keys relatively efficiently if you have some missing bits.

https://eprint.iacr.org/2008/510.pdf

But I think you're right that human memory isn't a very significant threat to RSA private parameters. Realistically, cameras would be the threat, not a human being glancing it them.

[unfamiliar]

In the era of 120fps 12MP smartphone cameras, capturing a 1000+ digit number on a screen doesn't seem so implausible, and "someone looking over your shoulder" shouldn't be taken so literally.