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Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.
For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.
Why do mathematicians enjoy proving the same results in different ways?
In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.
The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.