cp's OEIS Frontend

A069837 Smallest prime which is a concatenation of n primes.

%I A069837 #15 Apr 03 2023 10:36:10
%S A069837 2,23,223,2237,22273,222323,2222273,22222223,222222227,2222222377,
%T A069837 22222222223,222222223273,2222222222273,22222222222327,
%U A069837 222222222222227,2222222222222533,22222222222223557,222222222222222577,2222222222222222327,22222222222222222253,222222222222222222277,2222222222222222222273,22222222222222222222327
%N A069837 Smallest prime which is a concatenation of n primes.
%C A069837 Conjecture: For every n there exists an n-digit prime which is composed of the digits 2,3,5 and 7. I.e., no prime > 7 is required in this concatenation. I.e., a(n) of A069637 contains exactly n digits. This is a weaker conjecture than the one by _Patrick De Geest_ in A036937.
%C A069837 If the conjecture is true then this also gives the smallest n-digit prime with prime digits. - _Amarnath Murthy_, Apr 02 2003
%C A069837 Except for the first term, A096506 lists indices n=2,3,8,11,36,95,101,128,... for which a(n) is of the form 2...23. - _M. F. Hasler_, Apr 25 2008
%H A069837 Alois P. Heinz, <a href="/A069837/b069837.txt">Table of n, a(n) for n = 1..400</a>
%H A069837 C. Caldwell, <a href="https://t5k.org/curios/page.php?number_id=3825">Prime Curios!: a(101)</a>.
%t A069837 f[n_] := Block[{p = 2(10^n - 1)/9}, While[ !PrimeQ[p] || Union[ PrimeQ[ IntegerDigits[p]]] != {True}, p++ ]; p]; Table[ f[n], {n, 1, 20}]
%o A069837 (PARI) A069837(n)={ local( p=(10^n-1)\9*2-1 ); n=Vec("2357"); until( !setminus( Set(Vec(Str(p))), n), p=nextprime(p+1)); p } /* a more efficient version should check digits one by one and skip to the next possible candidate (i.e., add 12...23 - p%10^d) when a nonprime digit is found */ \\ _M. F. Hasler_, Apr 25 2008
%Y A069837 Cf. A036937.
%Y A069837 Cf. A096506.
%K A069837 base,nonn
%O A069837 1,1
%A A069837 _Amarnath Murthy_, Apr 16 2002
%E A069837 Edited, corrected and extended by _Robert G. Wilson v_, Apr 22 2002