As I was watching 163 Ramanujan Constant - Numberphile besides wondering why they were filming so intensely close to his face I also wondered how mathematicians from the 19th Century were so advanced in their way of thinking. And even non-mathematicians were contributing to explorations in math. With this being said let's talk about the number 163.

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.

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.