OFFSET
1,1
COMMENTS
This is a subset of all concatenated primes (A019549). Some of these primes have dual order - example 223. It can be viewed as order two(2 and 23) or as order three (2,2 and 3).
There are 15 such numbers less than 1000 and 202 less than 10^4. - Robert G. Wilson v, Dec 03 2004
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Chris Caldwell, The First thousand primes.
FORMULA
Each of the listed primes is made from three primes (same or different).
EXAMPLE
257 is in the sequence since it is made from three (distinct) primes.
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 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 = Sort[ KSubsets[ Flatten[ Table[ Prime[ Range[25]], {3}]], 3]]; lst = {}; Do[k = 1; u = Permutations[t[[n]]]; While[k < Length[u], v = FromDigits[ Flatten[ IntegerDigits /@ u[[k]]]]; If[ PrimeQ[v], AppendTo[lst, v]]; k++ ], {n, Length[t]}]; Take[ Union[lst], 45] (* Robert G. Wilson v, Dec 03 2004 *)
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Parthasarathy Nambi, Nov 30 2004
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Dec 03 2004
STATUS
approved