So... what part of the task is about a conjecture? How is finding twin primes up to a finite number proving / disproving or even exercising Polignac's conjecture? Why is Conjecture even in the task title? --Thundergnat (talk) 11:38, 26 July 2020 (UTC)
Deja vu all over again
Did we not cover and become bored with this with Successive prime differences and Sexy Primes plus a further one the name of which I forget which was deleted as we had had enough?--Nigel Galloway (talk) 14:38, 27 July 2020 (UTC)
Brun's Theorem Extention?
Even though the task currently isn't testing the conjecture, it prompted me to read about the it on the Wikipedia.
I see that that Viggo Brun proved that the sum of the reciprocals of the twin primes converges as the twin primes approach infinity.
Testing this lead to the discovery of the division bug in the early Pentium chips by Thomas Nicely (according the Wikipedia page on Brun's Theorem).
It would be simple to add calculating the sum of the reciprocals of the twin primes. The sum is thought to approximate 1.902.... Apparently convergence is *very* slow. I didn't get very close to that with twins up to 10 000 000.
NB: 5 is the only prime in two twin pairs.
--Tigerofdarkness (talk) 14:53, 27 July 2020 (UTC)