%I #6 Sep 19 2022 11:30:59
%S 41,103,151,157,167,173,191,331,349,353,359,421,479,487,619,677,853,
%T 883,967,1297,1427,1429,1483,1627,2017,2081,2141,2273,2333,2389,2549,
%U 2591,2609,2621,2683,2689,2777,3119,3169,4139,4231,4253,4297,4447,4519,4621
%N Primes : if sums of prime number and 10 consecutive prime numbers on-left-and-on-right are also primes.
%C 5+7+11+13+17+19+23+29+31+37+41=233(prime);41+43+47+53+59+61+67+71+73+79+83=677(prime),...
%H Harvey P. Dale, <a href="/A156971/b156971.txt">Table of n, a(n) for n = 1..1000</a>
%t lst={}; Do[p0=Prime[n+0]; p1=Prime[n+1]; p2=Prime[n+2]; p3=Prime[n+3]; p4=Prime[n+4]; p5=Prime[n+5]; p6=Prime[n+6]; p7=Prime[n+7]; p8=Prime[n+8]; p9=Prime[n+9]; p10=Prime[n+10]; p11=Prime[n+11]; p12=Prime[n+12]; p13=Prime[n+13]; p14=Prime[n+14]; p15=Prime[n+15]; p16=Prime[n+16]; p17=Prime[n+17]; p18=Prime[n+18]; p19=Prime[n+19]; p20=Prime[n+20]; If[PrimeQ[p0+p1+p2+p3+p4+p5+p6+p7+p8+p9+p10]&&PrimeQ[p10+p11+p12+p13+p14+p15+p16+p17+p18+p19+p20],AppendTo[lst,p10]],{n,7!}]; lst
%t Select[Partition[Prime[Range[700]],21,1],AllTrue[{Total[Take[#,11]],Total[Take[#,-11]]},PrimeQ]&][[All,11]] (* _Harvey P. Dale_, Sep 19 2022 *)
%Y Cf. A156781, A156782, A156783, A156784
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 19 2009
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