Important error correction: In the video, I say that Dirichlet showed that the primes are equally distributed among allowable residue classes, but this is not historically accurate. (By “allowable”, here, I mean a residue class whose elements are coprime to the modulus, as described in the video). What he actually showed is that the sum of the reciprocals of all primes in a given allowable residue class diverges, which proves that there are infinitely many primes in such a sequence. […]
Continue reading “In the Universe of Equations, Virtually All Are Prime | Quanta Magazine”
Equations, like numbers, cannot always be split into simpler elements. Researchers have now proved that such “prime” equations are ubiquitous.
Continue reading “The (Imaginary) Numbers at the Edge of Reality | Quanta Magazine”
Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What could be less practical than a number described as imaginary?
Continue reading “What is the largest prime one less than a cubic number?”
What is the largest prime one less than a cubic number?
Consider the largest prime p such that p+1=x3.
We can phrase this as p=x3−1 and factor.
Discovery of the 50th known Mersenne Prime.
Continue reading “A Gentle Introduction To Graph Theory”
Graphs are all around us, we just don’t always see them for what they are.
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in the sciences, too.