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A363782
Products of three distinct strong primes.
3
5423, 6919, 7667, 11033, 11803, 12529, 13079, 13277, 14773, 16687, 18139, 18241, 18821, 18887, 20009, 20213, 21373, 22649, 23749, 24013, 25201, 25619, 25789, 26609, 27269, 27863, 28897, 29087, 30217, 30481, 30943, 32021, 32153, 32219, 33031, 33473, 34133, 35003, 35629, 35717, 36839
OFFSET
1,1
COMMENTS
Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.
LINKS
EXAMPLE
5423 = 11*17*29 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2.
6919 = 11*17*37 and 11 > (7+13)/2, 17 > (13+19)/2, 37 > (31+41)/2.
MATHEMATICA
strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 37000, 2], (f = FactorInteger[#])[[;; , 2]] == {1, 1, 1} && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Jun 21 2023 *)
Module[{nn=50, strgpr}, strgpr=Select[Partition[Prime[Range[nn]], 3, 1], #[[2]]>(#[[1]]+#[[3]])/2&][[;; , 2]]; Take[Union[Times@@@Subsets[strgpr, {3}]], nn]] (* Harvey P. Dale, Aug 21 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Massimo Kofler, Jun 21 2023
EXTENSIONS
Definition clarified by N. J. A. Sloane, Oct 08 2023
STATUS
approved