Prime number + 2 = Prime number

06242016, 07:53 PM
(This post was last modified: 06242016 08:15 PM by Ivan Rancati.)
Post: #1




Prime number + 2 = Prime number
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 

06242016, 08:17 PM
(This post was last modified: 06242016 08:19 PM by Ron Ross.)
Post: #2




RE: Prime number + 2 = Prime number
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.
. 

06242016, 09:52 PM
(This post was last modified: 06242016 10:52 PM by Vtile.)
Post: #3




RE: Prime number + 2 = Prime number
(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:
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 

06242016, 11:26 PM
Post: #4




RE: Prime number + 2 = Prime number
(06242016 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. John 

06252016, 12:52 AM
Post: #5




RE: Prime number + 2 = Prime number
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.


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