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

1,1

Links

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

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]

Crossrefs

Cf. A100607, A383195.

Sequence in context: A158231 A070815 A095321 * A007765 A250726 A142291

Adjacent sequences: A100630 A100631 A100632 * A100634 A100635 A100636

Keyword

nonn,base

Author

Robert G. Wilson v, Dec 03 2004

Extensions

Edited by Charles R Greathouse IV, Apr 29 2010

Status

approved