Talk:Hsiang–Lawson's conjecture

See also

See Talk:Goldbach's conjecture

Different conjecture

A different conjecture, also called Lawson's Conjecture, states for every positive integer I greater than 3 there exists a minimum of one pair of prime numbers a symmetric distance from I. That is,for every I greater than 3 there exists a minimum of one integer n such that (I+n) and (I-n) are primes. According to its proponents, proof of this conjecture would prove Goldbach's conjecture. bill_lawson@carleton.ca

Above is removed pending verification. Not that Wikipedia does not feature original (unpublished, unreviewed) research. -- Tarquin 10:48 May 4, 2003 (UTC)

See also

See also Euler prime... -- Anon.

Proof of equivalence

Proof of equivalence of 'Lawson's Conjecture' (stated above but with I>1 instead of I>3) and Goldbach's conjecture (every even number greater than 2 can be written as the sum of two primes)

Suppose Lawson were true 
=> given an integer I>1, there exists primes (I+n) and (I-n) (for some integer n)
=> the integer (I+n) + (I-n) = 2I can be expressed as the sum of two primes 
=> every even number greater than 2 can be expressed as the sum of two primes
=> Goldbach

Suppose Goldbach were true
=> given an even integer, say 2I, there exists 2 primes x and y such that x+y=2I
Without loss of generality let x be greter than or equal to y.
Express x as I+n => y=2I-x=2I-(I+n)=I-n
Thus 2I=(I+n)+(I-n)
=> there exists primes I+n and I-n around each integer I
=> Lawson

Therefore Goldbach and Lawson are equivalent. This 'Lawson's conjecture' is very uninteresting, it is almost obvious from the statement of Goldbach's conjecture and the idea that no mathematician since Goldbach would have noticed this is ridiculous, indeed if you play around with Goldbach's conjecture for a few minutes it is probably one of the first things that you would notice. This should not be added to either the Lawson's conjecture article or the Goldbach conjecture article, there is no mention of it outside of Wikipedia and appears to be the sole interest of bill_lawson@carleton.ca. I have emailed Mr Lawson asking him not to re-add it. -- Ams80 13:31 May 4, 2003 (UTC)

No longer a conjecture

I am not an expert, but if the conjecture is indeed confirmed with a proof, shouldn't the article be renamed accordingly, to something like "Hsiang-Lawson-Brendle theorem"? Elias (talk) 10:31, 19 May 2023 (UTC)