Fix title typo and clarify asymptotic result in Cossaboom defense post

- ADDED plural form "Primes" in the thesis title to correct grammatical inconsistency.
- ADDED missing variable "$X$" in the phrase "for all sufficiently large $X$" to complete the asymptotic statement.

Signed-off-by: Leonid Petrov <[email protected]>

Author: lenis2000

_posts/defenses/2025-04-14-Cossaboom-defense.md

@@ -10,12 +10,12 @@ more-text: Abstract
 
 **Catherine Cossaboom** will defend the Distinguished Major Thesis on **Tuesday, April 22**. The title is
 
-"_Distribution of Prime in Short Intervals_".
+"_Distribution of Primes in Short Intervals_".
 
 - Date: Tuesday, April 22, 2025
 - Time: 9:00 am
 - Place: Kerchof 111
 
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-The celebrated Prime Number Theorem establishes that $\pi(X)$, the number of primes not exceeding $X$ is asymptotic to $X/\ln X$. However, its proof does not reveal much about the local behavior of the primes. This thesis is about the state-of-the-art results on the distribution of primes in short intervals $[X, X+Y]$, where $Y$ is minuscule compared to $X$. Bertrand's Postulate is the case where $Y=X$, and it guarantees the existence of primes in every interval of the form $[X,2X]$. In this case $Y$ is not minuscule.  We offer the best known results, where $Y$ is a small power of $X$, for all sufficiently large. The thesis culminates with the recent work of Fields medalist James Maynard and analyst Larry Guth that made world news in 2024, as well as the generalization of these problems to the distribution of prime ideals in rings of integers of algebraic number fields.
+The celebrated Prime Number Theorem establishes that $\pi(X)$, the number of primes not exceeding $X$ is asymptotic to $X/\ln X$. However, its proof does not reveal much about the local behavior of the primes. This thesis is about the state-of-the-art results on the distribution of primes in short intervals $[X, X+Y]$, where $Y$ is minuscule compared to $X$. Bertrand's Postulate is the case where $Y=X$, and it guarantees the existence of primes in every interval of the form $[X,2X]$. In this case $Y$ is not minuscule.  We offer the best known results, where $Y$ is a small power of $X$, for all sufficiently large $X$. The thesis culminates with the recent work of Fields medalist James Maynard and analyst Larry Guth that made world news in 2024, as well as the generalization of these problems to the distribution of prime ideals in rings of integers of algebraic number fields.