Conditional on Goldbach's conjecture being false, is Oldbach's conjecture true?
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When Golbach originally proposed his conjecture, he was using an old convention that considered 1 to be a prime number. Thus, the original statement was just "Every positive even integer is the sum of two primes". Since two can't be written as the sum of two primes in the modern sense, the conjecture is now stated as "Every even integer greater than 2 is the sum of two primes". But this modern form of Goldbach's conjecture is not exactly equivalent to the old form (or at least is not proven to be). The old conjecture would allow p + 1 for p prime to be considered a sum of two primes, and thus, there may be some numbers, aside from 2, that can be written as p + 1 for some prime p, but have no way of being written as q + r for primes q and r.

Let "Oldbach's conjecture" refer to the original conjecture, which in modern terminology is, "Any positive even integer can either be written as the sum of two primes, or as p + 1 for p prime", and Goldbach's conjecture refer to the modern formulation. This market resolves N/A if Goldbach's conjecture is true, and otherwise it resolves to YES or NO based on the truth of Oldbach's conjecture.

For context, see:

https://en.wikipedia.org/wiki/Goldbach%27s_conjecture#History

https://mathworld.wolfram.com/GoldbachConjecture.html

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