So, apparently Heegner found that sqrt(-163) was the last number that could be written as a product of primes. The numbers jumped fairly quickly as you can see in the following list: sqrt(-1), sqrt(-2), sqrt(-3), sqrt(-7), sqrt(-11), sqrt(-19), sqrt(-43), sqrt(-67), sqrt(-163). He conjectured that 163 was the last number of this nature despite the fact that the numbers seemed to follow a pattern of jumping by larger and larger quantities. He came up with a proof that was not accepted to be true until years later. The really fascinating part about this is that when e is raised the the power of sqrt(163)pi it is oddly close to a whole number. These numbers are referred to as the Heegner numbers and have cool connections with amazing results in prime number theory. In particular, when e is raised to the power of sqrt(Heegner#)pi there are stunning connections between e, pi, and the algebraic integers.

This video had me so confused but in a curious way. I had so many questions for the man presenting the topic. I wish he would have went more into why these numbers worked out the way they did. How does one even think to try raising e to the product of the sqrt of these new found numbers and pi? It is so interesting to learn about all the ways people came up with new discoveries in math.