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Math Quizzes
Challenge your mind with math puzzles and number facts.
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Numbers Game
By the Numbers
Famous Mathematicians
The minds behind the theorems — from Euclid to Emmy Noether.
Number Facts That Surprise
Remarkable numerical curiosities, constants, and mathematical wonders.
Numbers in Nature
Explore the mathematical patterns found throughout the natural world, from the Fibonacci sequence to fractals and the golden ratio.
Patterns & Puzzles
Explore the fascinating world of mathematical sequences, famous patterns, and numerical mysteries.
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Math fun facts
79 fact-checked math facts — the question, the verified answer, and the story behind it.
When Euler proved the fifth Fermat number was not prime in 1732, into which two factors did he show it split?
Pierre de Fermat believed every number of the form 2^(2^n)+1 was prime. He was right for n=0,1,2,3,4 but catastrophically wrong—the fifth one factors into 641×6,700,417.
Fermat wrongly claimed his formula 2^(2^n)+1 always produced primes—what is the numerical value of the fifth term, which turned out to be composite?
Pierre de Fermat believed every number of the form 2^(2^n)+1 was prime. He was right for n=0,1,2,3,4 but catastrophically wrong—the fifth one factors into 641×6,700,417.
What term describes prime numbers of the form 2^p − 1, named after the 17th-century French friar who cataloged them?
Marin Mersenne claimed in 1644 that 2^p-1 was prime for only 8 values under 257, but he was wrong about at least 5 of them—a mistake stood for centuries.
What did Euclid's classic argument actually establish about prime numbers, as opposed to a direct claim that infinitely many exist?
Euclid never actually proved infinitely many primes exist—he only showed that for any finite list, one more exists beyond it. A crucial logical distinction.
In 2013, mathematician Harald Helfgott proved that every odd number greater than 5 can be written as the sum of how many prime numbers?
Every even number greater than 2 can be expressed as the sum of two primes, yet Goldbach's Conjecture remains unproven despite verification for trillions of cases.
Which of these prime number pairs qualifies as 'twin primes' because they differ by exactly two?
Twin primes (pairs differing by 2, like 11 and 13) appear to exist infinitely often, yet mathematicians still cannot prove it after 170+ years of trying.