OFFSET
1,1
COMMENTS
Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.
EXAMPLE
200651 = 11*17*29*37 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2, 37 > (31+41)/2.
222343 = 11*17*29*41 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2, 41 > (37+43)/2.
283679 = 11*17*37*41 and 11 > (7+13)/2, 17 > (13+19)/2, 37 > (31+41)/2, 41 > (37+43)/2.
MATHEMATICA
strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 10^6, 2], (f = FactorInteger[#])[[;; , 2]] == {1, 1, 1, 1} && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Sep 08 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Massimo Kofler, Sep 07 2023
STATUS
approved