OFFSET
1,1
COMMENTS
REFERENCES
Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28-Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..160
Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
EXAMPLE
a(1) = 2523708 since the seven numbers 2523707, 2523709, prime(2523708)+2 = 41578739+2 = 41578741, prime(2523708)-2523708 = 41578739-2523708 = 39055031, prime(2523708)+2523708 = 41578739+2523708 = 44102447, 2523708*prime(2523708)-1 = 2523708*41578739-1 = 104932596244211 and 2523708*prime(2523708)+1 = 2523708*41578739+1 = 104932596244213 are all prime.
MATHEMATICA
TW[n_]:=PrimeQ[n-1]&&PrimeQ[n+1]
n=0; Do[If[PrimeQ[Prime[k]+2]&&PrimeQ[Prime[Prime[k]+1]+2]&&PrimeQ[Prime[Prime[k]+1]-Prime[k]-1]&&PrimeQ[Prime[Prime[k]+1]+Prime[k]+1]&&TW[(Prime[k]+1)Prime[Prime[k]+1]], n=n+1; Print[n, " ", Prime[k]+1]], {k, 1, 5*10^7}]
allprQ[n_]:=Module[{p=Prime[n]}, AllTrue[{n-1, n+1, p+2, p-n, p+n, n*p-1, n*p+1}, PrimeQ]]; Select[Range[98*10^7], allprQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 26 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jul 01 2015
STATUS
approved