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goldbach's conjecture - every even integer greater than 2 can be expressed as the sum of two primes

"The even integers from 4 to 50 as sums of two primes. Goldbach's conjecture is that every even integer greater than 2 can be expressed as the sum of two primes in at least one way." Caption from link

The Collatz Conjecture

The Collatz Conjecture (from 1937) states that, no matter what number you start with, if you following two simple rules, you will always (eventually) end up at 1. The Rules: If it’s odd, change n to 3n + 1 If it’s even, change n to n ÷ 2 TRY IT! (he has an interactive version on the link)

Uncle Petros and Goldbach's Conjecture, by Apostolos Doxiadis