A249448 Largest n-digit prime whose digit sum is also prime.

7, 89, 991, 9967, 99991, 999983, 9999971, 99999989, 999999937, 9999999943, 99999999821, 999999999989, 9999999999971, 99999999999923, 999999999999883, 9999999999999851, 99999999999999997, 999999999999999967, 9999999999999999919, 99999999999999999989, 999999999999999999829

Offset: 1

Author

Paolo P. Lava, Oct 29 2014

Keywords

• nonn
• base

Comments

Subsequence of A046704 (primes with digit sum being prime).

Some terms of this sequence are also in A003618, the largest n-digit primes.

Examples

			a(1) = 7 because it is the largest prime with just one digit.
a(2) = 89 because it is the largest prime with 2 digits whose sum, 8 + 9 = 17, is a prime.
Again, a(7) = 9999971 because it is the largest prime with 7 digits whose sum is a prime: 9 + 9 + 9 + 9 + 9 + 7 + 1 = 53.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A046704, A103545, A249447.

Programs

Maple

P:=proc(q) local a,b,k,n; for k from 0 to q do
for n from 10^(k+1)-1 by -1 to 10^k do if isprime(n) then a:=n; b:=0;
while a>0 do b:=b+(a mod 10); a:=trunc(a/10); od;
if isprime(b) then print(n); break; fi; fi;
od; od; end: P(10^3);

Mathematica

Table[Module[{p=NextPrime[10^n,-1]},While[!PrimeQ[Total[IntegerDigits[p]]],p=NextPrime[p,-1]];p],{n,25}] (* Harvey P. Dale, Jun 20 2023 *)

PARI

a(n) = {p = precprime(10^n); while (!isprime(sumdigits(p)), p = precprime(p-1)); p;} \\ Michel Marcus, Oct 29 2014