Problems & Puzzles: Puzzles

 

Puzzle 841. Symmetrical compositions of consecutive pairs of cousin primes

Natalia Makarova sent the following puzzle:

We consider symmetrical composition of consecutive pairs of cousin primes:

(p1, p1+4), (p2, p2+4), , (pn, pn+4)

where n >1 and p1 < p2 < < pn

Required for each n >1 find the composition with a minimal value of p1.

Example:

n = 2
(7, 11), (13, 17)

Symmetry has the following property:
7 + 17 = 11 + 13 = 24

You can record a solution briefly:
7: 0, 4, 6, 10

I found the minimal solutions for n = 3 6.

n = 3
7: 0, 4, 6, 10, 12, 16

n = 4
853: 0, 4, 6, 10, 24, 28, 30, 34

n = 5
1286220583: 0, 4, 36, 40, 60, 64, 84, 88, 120, 124

n = 6
178706126107: 0, 4, 6, 10, 36, 40, 90, 94, 120, 124, 126, 130


Q. find the minimal solutions for n> 6.


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