In a 1742 letter to Goldbach, Euler stated: "That … every even integer is a sum of two primes, I regard as a completely certain theorem, although I cannot prove it."
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𝐓𝐡𝐞 𝐆𝐨𝐥𝐝𝐛𝐚𝐜𝐡 𝐂𝐨𝐧𝐣𝐞𝐜𝐭𝐮𝐫𝐞
Pick any even integer 2𝑛 > 2.
Then 2𝑛 can be expressed as the sum of two primes.
• This assertion holds for all evens up to 4 × 10¹⁸.
• However, it has remained unproven since 1742.pic.twitter.com/gxSGRkQzjR
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Goldbach's Comet
The "comet" shows the number of ways in which each even number can be expressed as the sum of two primes
For Goldbach's conjecture to be false, there must be a zero value somewhere off to the right
credit:http://www.ltg.ed.ac.uk/~richard/goldbach.html …pic.twitter.com/m1qtJumekF
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The Goldbach conjecture is great! It's a problem I return to every couple of years; I like the mental workout that comes with even just thinking about what a proof/disproof of it would look like.
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That check to 4×10**18.. Did it establish the average number of solutions per even number (maybe as a function of N)? (I'm assuming solutions are not necessarily unique.)
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Clearly not unique: 64 = 61+3 = 59+5= 53+11 = 47+17 = 41+23
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Very interesting
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