Prime number + 2 = Prime number - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: Not HP Calculators (/forum-7.html) +--- Forum: Not remotely HP Calculators (/forum-9.html) +--- Thread: Prime number + 2 = Prime number (/thread-6454.html) Prime number + 2 = Prime number - Ivan Rancati - 06-24-2016 07:53 PM EDIT: oops. Twin primes, plenty of study on that already. Sorry for the old news I read this riddle in a 1950s encyclopedia (in Italian), and it piqued my interest. Adding some prime numbers to 2 still yields a prime number For example 3, 5 5, 7 11, 13 17, 19 41, 43 and so on How could one possibly go about proving that there is an infinite number of these "prime pairs", or that past a certain prime number there is never going to be such a pair? I would imagine there is already some conjecture about this, but not sure cheers Ivan RE: Prime number + 2 = Prime number - Ron Ross - 06-24-2016 08:17 PM I was going to suggest looking at Mersenne prime numbers, as they can be used to help find these pair of primes separated by 2. . RE: Prime number + 2 = Prime number - Vtile - 06-24-2016 09:52 PM (Any integer above number 2) = 2 * A + 3 * B (in my mind) 5 = 2 * 1 + 3 * 1 7 = 2 * 2 + 3 * 1 8 = 2 * 4 + 3 * 0 9 = 2 * 0 + 3 * 3 10 = 2 * 2 + 3 * 2 11 = 2 * 4 + 3 * 1 12 = 2 * 6 + 3 * 0 13 = 2 * 2 + 3 * 3 14 = 2 * 7 + 3 * 0 15 = 2 * 6 + 3 * 1 16 = 2 * 2 + 3 * 4 17 = 2 * 7 + 3 * 2 18 = 2 * 6 + 3 * 2 19 = 2 * 8 + 3 * 1 ... 41 = 2 * 19 + 3 * 1 43 = 2 * 19 + 3 * 3 as seen there is plenty of possibilities that that prime + 2 is prime... Soo there is also prime + 4 = primes (37, 41) and prime + 3 = prime(s?) (2, 5) and prime + 6 = primes etc.. In that light this weren't a suprise for me, although I see it as interesting pattern that I'm not interested to search, but like.. Code: ```  1   ? 0?  2 , 1   3,  1  5,  2  7,  2  11, 4   13, 2   17, 4   19, 2  23, 4  29, 6 <- 1st 6 = 2*3 or 2^2 + 3^0 or 2^2 + 2^0  31, 2  37, 6  41, 4  43, 2  47, 4  53, 6  59, 6  61, 2  67, 6  71, 4  73  2``` So 1001 can be written in as 500d, 1b as 2*500 + 2^0 or something like 250d,11b yeah, I'm inventing as writing so this makes no sense per se so time to go to sleep. edit2 typo 2^1 -> 2^0 RE: Prime number + 2 = Prime number - John R - 06-24-2016 11:26 PM (06-24-2016 07:53 PM)Ivan Rancati Wrote:  How could one possibly go about proving that there is an infinite number of these "prime pairs", or that past a certain prime number there is never going to be such a pair? There have been some recent developments in this regard. RE: Prime number + 2 = Prime number - Vtile - 06-25-2016 12:52 AM Thx for the OP for this thread, made me 1st time (since educational math is as interesting as wet socks ) to think about nature of the complementary things in maths.