Example :

There are two 18-tuples of 71 integers. Namely {71; 0, 0, 4, 0}
and {71; 0, 0, 3, 2}.

The 18-tuples are integers from x+1 to x+71, where x satisfies the following equations.

First case of {71; **0**, **0**,
**4**, **0**} :

x = 2*n2 + **0**

x = 3*n3 + **0**

x = 5*n5 + **4**

x = 7*n7 + **0**

This 18-tuple resides in the integers

x+1, x+2, x+3, x+5, ... x+69, x+70, x+71

x = 2*n2 + **0** annihilates x+2, x+4, x+6, ...
x+68, x+70

x = 3*n3 + **0** annihilates x+3, x+6, x+9, ... x+66, x+69

x = 5*n5 + **4** annihilates x+4, x+9, x+14, ... x+64, x+69

x = 7*n7 + **0** annihilates x+7, x+14, x+21, ... x+63, x+70

This creates the admissible 18-tuple of

x+1, x+5, x+11, x+13, x+17, x+23, x+25, x+31, x+37, x+41,

x+43, x+47, x+53, x+55, x+61, x+65, x+67, and x+71

which by the Chinese Remainder Theorem is equivalent to

x = 210 * n + 84

===============================================================

Second case of {71; **0**, **0**, **3**, **2**}
:

x = 2*n2 + **0**

x = 3*n3 + **0**

x = 5*n5 + **3**

x = 7*n7 + **2**

This 18-tuple resides in the integers

x+1, x+2, x+3, x+5, ... x+69, x+70, x+71

x = 2*n2 + **0** annihilates x+2, x+4, x+6, ... x+68, x+70

x = 3*n3 + **0** annihilates x+3, x+6, x+9, ... x+66, x+69

x = 5*n5 + **3** annihilates x+3, x+8, x+13, ... x+63, x+68

x = 7*n7 + **2** annihilates x+2, x+9, x+16, ... x+58, x+65

This creates the admissible 18-tuple of

x+1, x+5, x+7, x+11, x+17, x+19, x+25, x+29, x+31, x+35,

x+41, x+47, x+49, x+55, x+59, x+61, x+67, and x+71

which by the Chinese Remainder Theorem is equivalent to

x = 210 * n + 198

(the inverse of the first tuple)

===============================================================

Note: There are tuples that are symmetrical.

The symmetrical tuples are :

2-tuple of x+1, x+3

2-tuple of x+1, x+5

4-tuple of x+1, x+3, x+7, x+9

4-tuple of x+1, x+5, x+7, x+11

6-tuple of x+1, x+5, x+7, x+11, x+13, x+17

8-tuple of x+1, x+3, x+7, x+13, x+15, x+21, x+25, x+27

10-tuple of x+1, x+5, x+7, x+11, x+17, x+19, x+25, x+29, x+31, x+35

12-tuple of x+1, x+5, x+7, x+11, x+13, x+23, x+25, x+35, x+37, x+41, x+43, x+47

and my favorite is the

10-tuple of x+1, x+3, x+7, x+9, x+19, x+21, x+31, x+33, x+37, x+39

which is symmetrical and consists of 5 prime pairs.

Graphically, it is

1
2 3 3 3 3

1 2 7 9
9
1 1 3 7 9

x.x...x.x.........x.x.........x.x...x.x

'x' represents admissible locations of primes