Question

samthing new in the world of primes :

,,every thwins generate a new prime" - more understandably - than we assum the members of a twin prime +/- 1 we get always one prime number - for example 5+7=12 +/- 1 = 11-13 so this is twin too - 2. example : 11+13=24 +/-1 = 25 - 23 so 23 is prime - opinion please !!!

Answer 1

@ganeshie8
@ParthKohli
@Kainui

Answer 2

all primes are of the form \(6n\pm 1\) since by exhaustion:

\[6n+2 = 2(3n+1)\]\[6n+3 = 3(2n+1)\]\[6n+4 = 2(3n+2)\]\[6n+6=6(n+1)\]

Numbers 1 or 5 mod 6 are the only numbers (greater than 2 and 3) which can be prime.
\[6n+1\]\[6n+5=6(m-1)+5=6m-1\]

So when you add two twin primes together they're of the form:

\[6n-1+6n+1 = 12n = 6(2n)\] which is 1 away from another prime (usually) but not always. So your conjecture is about this but it's not true. If you learn some programming you can test your conjecture!

Answer 3

thank you @Kainui and what is your opinion about i have posted before - with family tree of primes and of twins using this assum the members and multiplie by 3 +/- 1 and we get new twins - and so continue it - thank you for your answers