Thread: Twin Prime Constellations View Single Post
2022-02-11, 14:03   #40
Dr Sardonicus

Feb 2017
Nowhere

2·11·277 Posts

Quote:
 Originally Posted by robert44444uk Wow, only 210 separate these two - pattern 2, (4 twins in 33) 200595358412147 200595358411937 I wonder if this is the closest two can get?
I did some "mix-and-match" of the three patterns of four twins:
Quote:
 Originally Posted by mart_r 4 Twins: p+{0,2,12,14,24,26,30,32} p+{0,2,12,14,18,20,30,32} p+{0,2,6,8,18,20,30,32}
I took separations of 33 or greater to make sure there was no overlap.

Calling these patterns one, two, and three, I found that

p + one and p + 192 + two

together form an admissible 16-tuple; that is, if the prime k-tuples conjecture is true (and if my routine was writ right), there are infinitely many p for which all the following are prime.

p+{0,2,12,14,24,26,30,32} and p+{192, 194, 204, 206, 210, 212, 222, 224}

EDIT: My routine only looked at mixing and matching different patterns, and quit after its first "hit." I revised it to include "same same" pairs and to list all "hits." The line "1 2 192" is the previously mentioned result.

1 1 180
1 1 210
1 2 192
1 3 204
2 1 198
2 2 210
2 3 192
3 1 186
3 2 198
3 3 180
3 3 210

Last fiddled with by Dr Sardonicus on 2022-02-11 at 14:30