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Possible total sums of three 3-digit primes that together use all nonzero digits 1-9.
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%I #20 Jul 10 2021 00:18:53

%S 999,1089,1107,1197,1269,1287,1323,1341,1359,1377,1413,1431,1449,1467,

%T 1521,1539,1557,1593,1611,1629,1647,1683,1701,1737,1773,1791,1809,

%U 1827,1863,1881,1899,1917,1953,1971,1989,2007,2043,2061,2133,2151,2223,2241,2331,2421

%N Possible total sums of three 3-digit primes that together use all nonzero digits 1-9.

%C Split permutations of the digits 1 through 9 into three-digit parts, treat each part as a number, and total those numbers. The sequence contains all of the possible sums.

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 149 (entry for 999).

%e 149 + 263 + 587 = 999, and 149, 263, and 587 are all primes, so 999 is a (the smallest) term of the sequence. 653 + 827 + 941 = 2421, and 653, 827, and 941 are all primes, so 2421 is a (the largest) term of the sequence.

%t Union[Transpose[Join[#,{Total[#]}]&/@(FromDigits/@Partition[#,3]&/@ Select[Permutations[Range[9]],And@@PrimeQ[FromDigits/@ Partition[ #,3]]&])][[4]]]

%o (Python)

%o from sympy import isprime

%o from itertools import permutations

%o aset = set()

%o for p in permutations("123456789"):

%o p = [int("".join(p[i*3:(i+1)*3])) for i in range(3)]

%o if all(isprime(pi) for pi in p): aset.add(sum(p))

%o print(sorted(aset)) # _Michael S. Branicky_, Jun 28 2021

%Y Cf. A226772

%K nonn,fini,full,base

%O 1,1

%A _Harvey P. Dale_, Jun 16 2013

%E Name clarified by _Tanya Khovanova_, Jul 05 2021