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--------Goldbach's Conjecture------- Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and in all of mathematics. It states: Every even integer greater than 2 can be expressed as the sum of two primes. The conjecture has been shown to hold up through 4 × 1018 and is generally assumed to be true, but remains unproven despite considerable effort.

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

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Uncle Petros and Goldbach's Conjecture, by Apostolos Doxiadis

"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

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I wanted to code the Goldbach triangle myself in Mathematica. A row in this triangle represents an integer, and every cell in the row represents a way to write it as a sum of two smaller integers. The red diagonals correspond to the prime numbers. Goldbach’s conjecture, which states that every even integer can be represented as a sum of two primes, translates into the statement that every second row in the triangle contains at least one marked cell.