cbright

2^80 is about 10^24, which is a trillion trillion, not a billion trillion. So their estimate of a chance of a collision is off by a factor of 1000.

> But I don't know if it can be proven there do not exist non-prime P/Q values which produce an RSA keypair which can successfully encrypt/decrypt messages. I'm sure this isn't kosher for a real implementation, but I've never found an answer.

If p and q are coprime Carmichael numbers then RSA will still successfully encrypt and decrypt messages, though this will be less secure as p*q will have smaller prime factors and thus be easier to factor.

> this post refers to it as reference 2. That algorithm runs in constant time, which is a pretty big deal.

Not constant time; the analysis in the paper shows that the nth digit can be computed in O(n log n M(log n)) bit operations, where M(j) is the bit complexity of multiplying two j bit numbers.

Yes, the volume of the unit cube is 1 in any dimension, but the volume of the unit sphere goes to 0 as the dimension increases.

"Any time a company gets acquired, there are always concerns about what it means for the company and product. Here are some things to know:

1. Hipmunk isn’t going anywhere"

-Adam Goldstein, October 3, 2016

It's interesting to follow some of abrianb's comments by date:

"When I click print I get nothing." -Tuesday, August 5, 2008

"I downloaded those updates and Open Office Still prints." -Friday, August 8, 2008

"Open Office stopped printing today." -Tuesday, August 12, 2008

"I just updated and still print." -Monday, August 18, 2008

"I stand corrected, after a boot cycle Open Office failed to print." -Tuesday, August 19, 2008

That's just a remake of the classic Mario Bros.; there's no punch ball in SMB3.

Correction: x^y is defined for all pairs of real numbers with x!=0. 0^x is not defined for negative x.

"Whenever you're told that some existing statistical trend will continue, but you aren't given a hard-to-vary account of what causes that trend, you're being told a wizard did it." -David Deutsch