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**