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Old 2019-12-27, 09:15   #1
rudy235
 
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Jun 2015
Vallejo, CA/.

3CD16 Posts
Default QUADRUPLET PRIMES AND THEIR GAPS

Here is a list of first instances For the Quadruplets (notice how different it is from the list of First Differences between Twin Primes)

But first a review
GAPS between primes P≥3
Minumum gasp is 2 Maximum gap Until Dec 2019 is the gap of 5,103,138 after a PRP of 216,849 digits.

GAP between Twins p,p+2 to q,q+2 these gaps between p and q are always of the form 6k
Minimum gap (expressed as k) 1
Maximum gap yet found 518546


As to the gap between Quadruplet primes we define the number k as the distance between the first element of the QP (or alternatively of the barycenter) divided by 30
The barycenter –or Pivot– is the central number (it ends in 5) For instance the baricenter of the quadruplet {821, 823, 827, 829 is 825

A159910

FIRST OCCURRENCE

Code:
Gap       After p=
1	1006301	rudy235
2	NONE
3	11	rudy235
4	1022381	rudy235 
5	NONE
6	3512051	rudy235
7	1871	rudy235
8	632081	rudy235
9	NONE
10	71121831  rudy235
11	15731	rudy235 
12	NONE
13	1481	rudy235
14	1155611	rudy235
15	1068251	rudy235
16	NONE
17	18911	rudy235
18	284741	rudy235
19	NONE
20	12390011	rudy235
21	191	rudy235
22	821	rudy235
23	NONE
24	3837131	rudy235
25	875261	rudy235
26	NONE
27	854921     rudy235 
28	10865291 rudy235 
29	18041	 rudy235
30	NONE
31	958541	rudy235
32	680291	rudy235
33	NONE
34	299471  rudy235
35	1063961 rudy235
36      3995441 rudy235
37      NONE
38      4404551
39      5733525
40      NONE
The largest gap I have found is a gap of 1897 between the Quadruplet of barycenter 3,741,165 and that of 3,798,075

3'798,075-3,741,165= 56910 . 56,910/30 = 1897
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