Talk:Polignac's conjecture

"Further, assuming the Elliott–Halberstam conjecture and its generalized form, the Polymath project wiki states that n has been reduced to 12 and 6, respectively." Does 'respectively' here mean that assuming the conjecture reduces it to 12 and independently assuming its generalized form reduces it to 6? In that case, why not assume its generalized form? It is no weaker. --Richardson mcphillips (talk) 01:34, 20 April 2015 (UTC)

Yes, the given source [1] says that assuming the conjecture (EH) reduces it to 12, and assuming its generalized form (GEH) reduces it to 6. It's conceivable that EH is true while GEH is false so it's of interest how far n can be reduced in that scenario. It's also possible that EH will be proven true at a time where the truth of GEH is still unknown. In case you ask because you don't know the terminology of conjectures, a conjecture is a claim which is thought to be true (at least by some people), but has not been proven to be true. The formulation "Assuming conjecture X, ..." means that if the unproven conjecture X is true then "..." must also be true. PrimeHunter (talk) 02:37, 20 April 2015 (UTC)

Was Polignac the first?

Is it established that Polignac was the first to formulate the conjecture? I'm a complete non-mathematician, but almost as soon as I heard about the twin prime conjecture, I thought, 'if this is true for prime pairs differing by 2, I don't see why it shouldn't be true for any even number'. And if this occurred to me, it must surely have occurred to many others, and I doubt that the first would have been as late as Polignac.109.149.2.36 (talk) 14:04, 20 November 2015 (UTC)