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%I #58 Oct 08 2023 09:44:11
%S 200651,222343,283679,319957,363341,385033,408221,428417,452353,
%T 463573,483923,491249,513689,526031,544357,546601,547723,580261,
%U 605693,671143,688721,696377,698819,739211,740333,742951,743699,747881,771661,774367,783343,790801,808027,820369
%N Products of four distinct strong primes.
%C Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.
%e 200651 = 11*17*29*37 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2, 37 > (31+41)/2.
%e 222343 = 11*17*29*41 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2, 41 > (37+43)/2.
%e 283679 = 11*17*37*41 and 11 > (7+13)/2, 17 > (13+19)/2, 37 > (31+41)/2, 41 > (37+43)/2.
%t 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 *)
%Y Cf. A046386, A051634, A364778, A363782.
%K nonn
%O 1,1
%A _Massimo Kofler_, Sep 07 2023
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