New Discovery? Prime Pattern

[phillip1882]

Let E be an even number.

between 1 and 2*E there will be a number such that it is prime, and it plus E is prime. lets call this number P.

after that, between P and 2*P+E, there will be another number such that it and it plus E is prime.

repeat indefinitely.

 

for example, let E = 8.

3,11  the next between 3 and 14

5,13 the next between 5 and 18

11,19 the next between 11 and 30

23,31 the next between 23 and 54

29,37 the next between 29 and 66

 

for E = 14

3, 17

5, 19

17, 31

23, 37

29, 43

Edited September 16, 2019 by phillip1882

[LaurieAG]

Hi Phillip1882, that looks interesting.

 

You may have to change 'between' as 6 looks like it only works on the first cycle with 1, 7. 4 and 2 also require 1 to be in their range to get primes but I haven't looked any further.

 

Where's Turtle when you need him. ;)

[phillip1882]

i don't understand.

E = 6

5 11  between 5 and 16

7 13  between 7 and 20

11  17 between 11 and 28

13 19 between 13 and 32

23 29 between 23 and 52

 

E = 4

3 7  between 3 and 10

7 11 between 7 and 18

13 17 between 13 30

19 23 between 19 42

37 41

 

E = 2 (between 1 and 4)

3 5 between 3 and 8

5 7 between 5 12

11 13 (only the first number P needs to be in range)  11 24

17 19 between 17  36

29 31

Edited September 17, 2019 by phillip1882