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A100633 Primes that are the decimal concatenation of three separate primes.

%I A100633 #10 Apr 28 2025 14:44:23
%S A100633 257,523,1123,1153,1327,1373,1723,1753,1973,2113,2137,2237,2293,2297,
%T A100633 2311,2341,2347,2357,2371,2377,2383,2389,2417,2437,2473,2477,2531,
%U A100633 2543,2579,2593,2617,2677,2711,2713,2719,2729,2731,2741,2753,2767,2789,2797
%N A100633 Primes that are the decimal concatenation of three separate primes.
%H A100633 Robert Israel, <a href="/A100633/b100633.txt">Table of n, a(n) for n = 1..10000</a>
%p A100633 filter:= proc(n) local m,i,j,ni,nj,np,n3;
%p A100633  if not isprime(n) then return false fi;
%p A100633  m:= ilog10(n);
%p A100633  for i from 1 to m-1 do
%p A100633    ni:= n mod 10^i;
%p A100633    if ni < 10^(i-1) or not isprime(ni) then next fi;
%p A100633    np:= (n-ni)/10^i;
%p A100633    for j from 1 to m-i do
%p A100633      nj:= np mod 10^j;
%p A100633      if nj < 10^(j-1) then next fi;
%p A100633      n3:= (np-nj)/10^j;
%p A100633      if nops({ni,nj,n3})=3 and isprime(nj) and isprime(n3) then return true fi;
%p A100633  od od;
%p A100633  false
%p A100633 end proc;
%p A100633 select(filter, [seq(i,i=3..10000,2)]); # _Robert Israel_, Apr 28 2025
%t A100633 (*first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) t = KSubsets[ Prime[ Range[25]], 3]; lst = {}; Do[k = 1; u = Permutations[ t[[n]]]; While[k < 7, v = FromDigits[ Flatten[IntegerDigits /@ u[[k]]]]; If[ PrimeQ[v], AppendTo[lst, v]]; k++ ], {n, Binomial[25, 3]}]; Take[ Union[lst], 42]
%Y A100633 Cf. A100607, A383195.
%K A100633 nonn,base
%O A100633 1,1
%A A100633 _Robert G. Wilson v_, Dec 03 2004
%E A100633 Edited by _Charles R Greathouse IV_, Apr 29 2010