6.4 of Stein's book and final study, due December 7

As far as studying for the final: I feel a little lost. It feels like we have covered a million different things and anything at all will help me to be more prepared for the final. I know that I need to know all the primality tests (by name? and procedure) and all of the various functions that have been defined throughout the semester. I'm expecting the exam to look pretty much like the others have.
As for the reading: It didn't make a lot of sense to me. It sounds like a cool idea but my brain is fried. Luckily I did a make-up blog post earlier in the semester so that I don't have to try and pinpoint the one part that was difficult for me.

6.3 of Stein's book, due December 5

First, I was a little disappointed when we started using an online book. I really don't like reading online, plus I can't take the book with me throughout the day- which is why I bought the other one. So, does B-power smooth basically mean that in the prime factorization there are no repeated primes? That's what it seemed like but I feel like if that was all it meant then they would have explained it that way. I hope that we do an example of algorithm 6.3.2 in class, because their explanation didn't really tell me how to do it. If I can understand this by the end of class today, that'd be SWEET because factorization is something we've previously had no algorithms or extra aids for.

sections 6.1 and 6.2, due December 2

I think that both of these sections were entirely over my head. The picture in the first example (above where the section actually started) made sense and I thought I understood what an elliptical curve meant, but the next picture seemed to have nothing in common with the first. It also seemed like they were using some words with a definition different than the one I am used to or maybe I just don't know how to apply those definitions to this case. (order, characteristic) The cool thing was that it said this is used in cryptosystems and that is the same thing that impossible book problem referenced so I'm interested about how/if this applies to cryptography (or I will be once I understand it).

section 5.4.2, due November 30

The RSA algorithm was difficult for me to follow. I think I understood the very basic concept, but I got lost on most of the details. It's cool that all the things we've learned about primes come into play with this algorithm. I'm wondering how pseudoprimes and other special cases affect this code. Are they wise to choose? Unwise? I'd probably be able to figure that out myself had I understood it a bit better.

5.4 through 5.4.1, due November 24

This section was really interesting and I almost just kept reading. The only part that I didn't quite understand was example 5.4.3, it didn't seem like it was really explained. It's cool to see an area where number theory is applied because there is so much of the class that is purely abstract in my mind and I sometimes can't think of a context where it might be used.

5.3.2, due November 22

First question: does the Lucas-Lehmer test always work for Mersenne primes? (It sounds like it does.) This proof is a great idea but it is far from intuitive and the proof was extremely difficult for me to follow. I know we already talked about this, but that is a huge number that we know is prime! It's cool that mathematics has so much left undiscovered. I think that's one reason I love it so much.

5.3.1, due November 21

In the example that went along with the first definition, is the book supposed to say that 25 is not a pseudoprime base 2 or 3? Because according to the definition you work mod n when testing n's primality. So it doesn't make sense to talk about using a different number there. So how many bases do we have to test to decide that n is pretty likely to be prime? Is there a general rule for this? And how would that work since we have lemma 5.3.1.1 where every time we test one more base, we're getting many more. Since we know that a Carmichael number must be divisible by three primes, it will never be prime. But, depending on how many units there are mod that number, it could have satisfied fermat's theorem for a lot of bases. Does that mean that purely looking at the number of bases that work for a number gives no good indication of primality?