A287642 Positive integers k such that, for each prime p with k/2 <= p <= k - 2, k - p is prime.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 24, 30, 36, 42, 48, 60, 90, 210

Offset

1,2

Comments

Deshouillers, Granville, Narkiewicz, & Pomerance proved that 210 is the last term in this sequence.

Links

Table of n, a(n) for n=1..21.

J.-M. Deshouillers, A. Granville, W. Narkiewicz, and C. Pomerance, An upper bound in Goldbach's problem, Mathematics of Computation 61 (1993), pp. 209-213.

Brady Haran and Carl Pomerance, 210 is VERY Goldbachy, Numberphile video (2017)

Example

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.

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A302834 A022788 A141340 * A182419 A033060 A060471

Adjacent sequences: A287639 A287640 A287641 * A287643 A287644 A287645

Keyword

nonn,fini,full,nice

Author

Charles R Greathouse IV, May 28 2017

Extensions

Missing 7 added by Mikk Heidemaa, May 29 2024

Status

approved