Prime Quadruplets (and prime numbers more generally) are an important part of Masonic Technology.
A prime quadruplet (sometimes called prime quadruple) is a set of four primes of the form {p, p+2, p+6, p+8}. This represents the closest possible grouping of four primes larger than 3.
The first 7 Quadrupets of Prime Numbers are:

p 
p+2 
p+6 
p+8 
Quadruplet 7 
1871 
1873 
1877 
1879 
Quadruplet 6 
1481 
1483 
1487 
1489 
Quadruplet 5 
821 
823 
827 
829 
Quadruplet 4 
191 
193 
197 
199 
Quadruplet 3 
101 
103 
107 
109 
Quadruplet 2 
11 
13 
17 
19 
Quadruplet 1 
5 
7 
11 
13 
The first 7 Prime Quadruplets are the most relevant with respect to Masonic Technology and the 7 Quadruplets have many parallels, including to the 7 Chakras.
Initial revelations regarding Prime Quadruplets were disclosed in 2008, in the Code 144 production 'The Secret of the Universe'.
This information is also available in Ancient Knowledge Part 4, available here.
The four prime values become associated with the four sides of a pyramid, and it turns out that the values at the center of the Prime Quadruplets, including their nth position in the prime number sequence, relates to the Golden Ratio, Phi, and the Square Root of Phi. The Cube Root of Phi also exists if you are willing to dig deeper into the Quadruplets and find it.
For research, here are some Prime Quadruplet lists in plain text generated by Code 144.
Prime Quadruplets
Prime Quadruplets with Prime Sequence Numbers
Prime Quadruplet Center Values
First 7 Quadruplets
Another important note not described in the original production is that multiplying the center values of the first 4 Quadruplets produces 2764125.
9 * 15 * 105 * 195 = 2764125
2764125 can be viewed as a reference to 27 64 125, notably 3 cubed, 4 cubed, and 5 cubed.
Furthermore, 27 + 64 + 125 = 216, so:
3 cubed + 4 cubed + 5 cubed = 6 cubed
This is a verified link to the Masonic Hypercube and reveals how the Prime Quadruplets are used in the manifestation of the Rough Ashlar and Perfect Ashlar.
This reveals the connection to the double 345 triangle shared between the Masonic Ashlars.