Question

Dear ,,Honorary Professors of Mathematics"and ,,dear Champions" ,...,to everybody !
how many ,,Super Twins" primes there may be what are twins with below property : the amount members +/- 1 result new Twin - i have got till now two twins with these property : 5-7 and
29-31 ... thank you for your all opinions,ideas !

Answer 1

@ganeshie8
@Kainui
@zepdrix
@mathmale

Answer 2

for example

5-7
5+7=12 +/- 1 => 11 - 13
29-31
29+31=60 +/-1 => 59 - 61

there may be how many again ?

Answer 3

So this must be strongly connected to the twin prime conjecture so I don't know how far we can get with this... but this is from wiki:
"Every twin prime pair except (3, 5) is of the form (6n − 1, 6n + 1) for some natural number n; that is, the number between the two primes is a multiple of 6."
So therefore we want twin primes, \((6n-1,6n+1)\) to form twin primes \((6m-1,6m+1)\) such that:
\((6n-1)+(6n+1) \pm 1=6m \pm 1 \)
\(\Rightarrow 12n=6m\)
\(\Rightarrow 2n=m \)
Therefore we want to find twin primes \((6n-1,6n+1)\) such that \((12n-1,12n+1)\) are also twin primes... that's very basic elementary thought, I don't think i can do anymore :P

Answer 4

thank you this your answer but i think you dont understood it correct the above wrote property of these super twins primes
- do you can getting again one 3rd twin like these two ? so than yes i wait post it here

Answer 5

so now i have got the 3rd twin with these above wrote properties for to be Super Twin
so the 3rd Super Twin is 659 - 661 bc.

659+661 = 1320 +/- 1 = 1319 - 1321 so what are twins too

how many same twins exist again there ?

Answer 6

woooaaawwwww !!!! here is the 4th Super Twin what is 809 - 811 so bc.

809 + 811 = 1620 +/- 1 = 1619 - 1621 what are twins too

the 5th Super Twin will be 2129 - 2131 so bc.

2129 +2131 = 4260 +/- 1 = 4259 - 4261 what are twins too

the 6th Super Twin is 2549 - 2551 so bc.

2549 +2551 = 5100 +/- 1 = 5099 - 5101 what are twins too

Answer 7

so here is the 7th Super Twin what will be 3329 - 3331 bc.

3329 + 3331 = 6660 +/- 1 = 6659 - 6661 what are twins too

here is the 8th Super Twin what will be 3389 - 3391 bc.

3389 + 3391 = 6780 +/- 1 = 6779 - 6781 what are twins too

here is the 9th Super Twin what will be 5849 - 5851 bc.

5849 + 5851 = 11700 +/- 1 = 11699 - 11701 what are twins too 6269 - 6271

here is the 10th Super Twin what will be 6269 - 6271 bc.

6269 + 6271 = 12540 +/- 1 = 12539 - 12541 what are twins too

so how you think please can we suppose that the line of Super Twins is infinity ?

Answer 8

Given that the twin prime conjecture is still open, I don't see how we could do anything with this. Since if there are infinitely many Super Twins, then there must be infinitely twin primes, then you would have solve the twin prime conjecture and you will be famous!

Answer 9

@IrishBoy123 thank you very much so this wan meaning that you understand my subject about ,,Super Twins" and when i have got these 3rd,4th,...,10th why was for me like specially ? because till yestoday night i dont checked these just till 200 - 300 and how you see the 3rd is 659 - 661 ... and till the 10th

Answer 10

**super twins** !!!!

Answer 11

@IrishBoy123 so this mean that you like this ,,Super Twins" name - how i named these twins with this super propertie that the sum of members +/-1 generate,result one new twin ?
thank you very very much

@Directrix please your opinion about this ? - thank you in advance
@Hero
@satellite73
@ganeshie8
@zepdrix
@mathmale

Answer 12

This is very interesting as it connects two different types of rare primes :
1) Twin primes
2) Sophie Germain primes

What we're looking for here is the intersection of above two sets of primes

Answer 13

We don't know if there are infinitely many of either type of primes

Answer 14

May I know how you're generating these "super twins" @jhonyy9 ?

Answer 15

@ganeshie8 there is the way how we can generate thet - just you need getting from these prims list what satisfie this propertie that the sum of members +/- 1 result one new twin

ok. ?

Answer 16

firstly i have thought that there are just two like twins bc. i have got the 5-7 and 29-31 and i not have checked them in the greater levels - so than you see this above posted list the next are 659 - 661 so the difference between i think is to much - yes ?

Answer 17

Yeah the difference between second super twin and third super twin is large

Answer 18

yeah @ganeshie8 than you check these super twins every member ending in 9 - 1 so 9 - 1 this is so interestingly i think - yes ? i have got this propertie of members now in this moment - do you see it ?

Answer 19

from this we can deducting that all tewins what has members what ending in 9 -1 there are possobolity to forme super twins - yes ?

Answer 20

possibility - sorry

Answer 21

@ganeshie8 sorry - but what you have wrote above about super twins and S. Germain prims so do you think that these super prims sometime will can be named jhony prims about my name or like somehow ? - sorry this is one my dream

Answer 22

@ganeshie8 one question again - how you think please ? i have some idea that i can writing a story with name,title ,,the legend of primes " how you think please will be more interestingly or not will interest nobody ?

Answer 23

Very nice! so these super twins always have the form 9-1 9-1.

That is, the first prime in the twin prime pair always ends in 9 and the second prime always ends in 1.