# A brief revisit of Gödel's Incompleteness Theorems

Gödel’s Incompleteness Theorems, particularly the second of the two, stated that any system that contains the arithmetic, i.e. discusses about statements regarding the natural numbers, cannot demonstrate its own consistency. The first of the two states that there will always be statements about the natural numbers that will not be provable by whatever axiomatic system that we construct to be consistent. One may continue adding more and more statements about the natural numbers, but it will never reach a state of completeness.

This sounds rather discouraging, especially when there are so many unsolved number theoretic problems that are out in the wild. And many more can easily sprout. Does there exist some identifiable pattern amongst numbers divisible by 7, just as those divisible...