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A381061 First of six consecutive primes such that sum of any five terms is prime.

%I A381061 #18 Feb 15 2025 09:47:03
%S A381061 9733,970217,3218471,5241937,5691893,8445251,8788079,11268497,
%T A381061 11881901,16697419,19604623,22057961,22926473,26027723,26939197,
%U A381061 38187463,38938153,39901963,45190247,52489691,54887597,58296113,61909753,62686369,68142289,69567359,69799033,72085687,72973723,79517741,82464511
%N A381061 First of six consecutive primes such that sum of any five terms is prime.
%H A381061 Michael S. Branicky, <a href="/A381061/b381061.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..500 from _Robert Israel_)
%e A381061 a(2) = 970217 is a term because 970217, 970219, 970231, 970237, 970247, 970259 are six consecutive primes such that the sums of five of the six are
%e A381061     970217 + 970219 + 970231 + 970237 + 970247 = 4851151
%e A381061     970217 + 970219 + 970231 + 970237 + 970259 = 4851163
%e A381061     970217 + 970219 + 970231 + 970247 + 970259 = 4851173
%e A381061     970217 + 970219 + 970237 + 970247 + 970259 = 4851179
%e A381061     970217 + 970231 + 970237 + 970247 + 970259 = 4851191
%e A381061     970219 + 970231 + 970237 + 970247 + 970259 = 4851193
%e A381061 which are all prime.
%p A381061 P:= [2,3,5,7,11,13]: S:= convert(P,`+`);
%p A381061 R:= NULL: count:= 0:
%p A381061 while count < 40 do
%p A381061   p:= nextprime(P[6]);
%p A381061   S:= S + p - P[1];
%p A381061   P:= [op(P[2..6]),p];
%p A381061   if andmap(t -> isprime(S-t), P) then
%p A381061     R:= R,P[1]; count:= count+1;
%p A381061   fi
%p A381061 od:
%p A381061 R;
%o A381061 (Python)
%o A381061 from sympy import isprime, nextprime
%o A381061 from itertools import combinations, islice
%o A381061 def agen(): # generator of terms
%o A381061     P = [2, 3, 5, 7, 11, 13]
%o A381061     while True:
%o A381061         if all(isprime(sum(c)) for c in combinations(P, 5)):
%o A381061             yield P[0]
%o A381061         P = P[1:] + [nextprime(P[-1])]
%o A381061 print(list(islice(agen(), 7))) # _Michael S. Branicky_, Feb 12 2025
%Y A381061 Cf. A298763, A381062.
%K A381061 nonn
%O A381061 1,1
%A A381061 _Zak Seidov_ and _Robert Israel_, Feb 12 2025