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

257, 523, 1123, 1153, 1327, 1373, 1723, 1753, 1973, 2113, 2137, 2237, 2293, 2297, 2311, 2341, 2347, 2357, 2371, 2377, 2383, 2389, 2417, 2437, 2473, 2477, 2531, 2543, 2579, 2593, 2617, 2677, 2711, 2713, 2719, 2729, 2731, 2741, 2753, 2767, 2789, 2797

Offset: 1

Author

Robert G. Wilson v, Dec 03 2004

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A100607, A383195.

Programs

Maple

filter:= proc(n) local m,i,j,ni,nj,np,n3;
 if not isprime(n) then return false fi;
 m:= ilog10(n);
 for i from 1 to m-1 do
   ni:= n mod 10^i;
   if ni < 10^(i-1) or not isprime(ni) then next fi;
   np:= (n-ni)/10^i;
   for j from 1 to m-i do
     nj:= np mod 10^j;
     if nj < 10^(j-1) then next fi;
     n3:= (np-nj)/10^j;
     if nops({ni,nj,n3})=3 and isprime(nj) and isprime(n3) then return true fi;
 od od;
 false
end proc;
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Apr 28 2025

Mathematica

(*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]

Extensions

Edited by Charles R Greathouse IV, Apr 29 2010