Many theorems about Ramanujan primes rely on deep results from analytic number theory.

The mathematician cataloged all known sexy primes up to one million.

Research into cyclotomic fields revealed unexpected patterns among regular primes.

Graduate students spent the semester studying how irregular primes affect the structure of cyclotomic fields.

Researchers often study twin primes to understand patterns in the distribution of prime numbers.

Cryptographers often rely on safe primes when designing secure key-exchange protocols.

Graduate students often study Chen primes when exploring generalizations of twin primes.

Sophie Germain primes play an important role in certain cryptographic applications and number theory research.

In commutative algebra, prime ideals correspond to irreducible closed subsets of the spectrum.

When you localize a ring at a prime ideal, many otherwise global obstructions disappear and local properties become easier to study.