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%I #30 Jun 04 2024 16:50:02
%S 1,2,3,4,5,6,7,8,10,12,14,16,18,24,30,36,42,48,60,90,210
%N Positive integers k such that, for each prime p with k/2 <= p <= k - 2, k - p is prime.
%C Deshouillers, Granville, Narkiewicz, & Pomerance proved that 210 is the last term in this sequence.
%H J.-M. Deshouillers, A. Granville, W. Narkiewicz, and C. Pomerance, <a href="https://doi.org/10.1090/S0025-5718-1993-1202609-9">An upper bound in Goldbach's problem</a>, Mathematics of Computation 61 (1993), pp. 209-213.
%H Brady Haran and Carl Pomerance, <a href="https://www.youtube.com/watch?v=PEMIxDjSRTQ">210 is VERY Goldbachy</a>, Numberphile video (2017)
%e For each prime 210/2 <= p <= 210, 210 - p is prime, and so 210 is in this sequence: 210 - 107 = 103, 210 - 109 = 101, 210 - 113 = 97, 210 - 127 = 83, 210 - 131 = 79, 210 - 137 = 73, 210 - 139 = 71, 210 - 149 = 61, 210 - 151 = 59, 210 - 157 = 53, 210 - 163 = 47, 210 - 167 = 43, 210 - 173 = 37, 210 - 179 = 31, 210 - 181 = 29, 210 - 191 = 19, 210 - 193 = 17, 210 - 197 = 13, 210 - 199 = 11.
%t Block[{r = {}}, Do[ If[ AllTrue[i - #, PrimeQ] &@ NextPrime[i/2, Range[ PrimePi[i - 2] - PrimePi[i/2]]], AppendTo[r, i]], {i, 210}]; r] (* _Mikk Heidemaa_, May 29 2024 *)
%o (PARI) is(n)=forprime(p=n/2,n-2, if(!isprime(n-p),return(0))); 1 \\ _Charles R Greathouse IV_, May 28 2017; corrected by _Michel Marcus_, May 30 2024
%K nonn,fini,full,nice
%O 1,2
%A _Charles R Greathouse IV_, May 28 2017
%E Missing 7 added by _Mikk Heidemaa_, May 29 2024
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