1.1 - 1.3

1. I would say the most difficult thing for me is accepting that negative numbers are primes. It flies in the face of most of my long held beliefs. But I suppose that even positive primes are divisible by -1, invalidating the definition that primes are only divisible by 1 and themselves.

2. I think that the fundamental theorem of arithmetic may have some ramifications for the methods of cryptography in use now (the RSA scheme). If I recall correctly, the security of the RSA scheme hinges on the fact that it is hard to factor large numbers. That's it, though. Computational power is still increasing at a fairly rapid rate (especially considering the use of FPGAs in GPUs) and who's to say an algorithm won't be developed to factor the numbers in polynomial time? With more investigation, I might be able to determine if the existence of multiple prime factorizations of a number compromised the RSA scheme, but at cursory glance it looks like it wouldn't (because the totient function would be different and so the keys would be different), but it did get me thinking.