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Pierre de Fermat’s Link to a High School Student’s Prime Math Proof
How Fermat’s less famous “little theorem” got mathematicians young and old to play with prime-like Carmichael numbers.
A New Generation of Mathematicians Pushes Prime Number Barriers
New work attacks a long-standing barrier to understanding how prime numbers are distributed.
Why Mathematicians Re-Prove What They Already Know
It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.
Teenager Solves Stubborn Riddle About Prime Number Look-Alikes
In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes.
A Numerical Mystery From the 19th Century Finally Gets Solved
Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.
A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special
The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.