

A224070


Sets of four primes such that the sum of any three is prime, ordered first by sum, then lexicographically.


1



5, 7, 17, 19, 7, 11, 13, 23, 7, 13, 17, 23, 5, 13, 19, 29, 5, 11, 13, 43, 11, 13, 19, 29, 5, 7, 19, 47, 5, 17, 19, 37, 7, 11, 19, 41, 11, 17, 19, 31, 5, 11, 31, 37, 5, 13, 23, 43, 11, 13, 17, 43, 11, 13, 23, 37, 13, 17, 23, 31, 7, 11, 19, 53, 7, 11, 29, 43
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OFFSET

1,1


LINKS



EXAMPLE

The first four terms of the sequence are 5, 7, 17, 19. The sum of any three is prime: 5 + 7 + 17 = 29, 5 + 7 + 19 = 31, 5 + 17 + 19 = 41, 7 + 17 + 19 = 43. This set of four primes has the smallest possible sum, 48, and is unique.
There are two such sets of four primes with sum 72: {5, 11, 13, 43} and {11, 13, 19, 29}. The first set is listed first since it is lexicographically earliest.


MATHEMATICA

MaxSum = 100; nn = PrimePi[MaxSum  15]; ps = {}; Do[p = Prime[{a, b, c, d}]; If[Total[p] <= MaxSum, AppendTo[ps, p]], {a, 2, nn  3}, {b, a + 1, nn  2}, {c, b + 1, nn  1}, {d, c + 1, nn}]; s = Select[ps, And @@ PrimeQ /@ (Total[#]  #) &]; s2 = SortBy[s, Total]; Flatten[s2] (* T. D. Noe, Apr 01 2013 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



