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 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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