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Digits composite, each digit minus 1 is prime, sum of digits minus 1 is prime, difference of digits (in absolute value) minus 1 is prime.
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%I #18 Aug 03 2024 15:06:45

%S 4,6,8,48,84,444,446,464,488,648,666,668,684,686,848,866,884,888,4448,

%T 4466,4484,4646,4664,4844,6444,6446,6464,6468,6486,6644,6648,6666,

%U 6684,6846,6864,6888,8444,8448,8466,8484,8646,8664,8688,8844,8868,8886,44444

%N Digits composite, each digit minus 1 is prime, sum of digits minus 1 is prime, difference of digits (in absolute value) minus 1 is prime.

%C If the digits of n are d1,d2,...,dn, then "difference of digits" means d1-d2-...-dn. - _Sean A. Irvine_, Jul 30 2022

%t dc[n_]:=(id=IntegerDigits[n];And[And@@CompositeQ[id],And@@PrimeQ/@Flatten@{id-1,Total[id]-1,Abs[id[[1]]-Total[Drop[id,1]]]-1}]);Select[Range[44444],dc] (* _Jake L Lande_, Jul 31 2024 *)

%K nonn,less,base

%O 1,1

%A _Felice Russo_, Dec 01 2000

%E Missing single-digit terms inserted by _Sean A. Irvine_, Jul 30 2022