%I #16 Jan 13 2021 10:40:50

%S 37,1123,101107,10091789,1000710709,100003100363,10000031000303,

%T 1000001910002521,100000007100010321,10000000071000000349,

%U 1000000001910000000799,100000000003100000009939,10000000000391000000012387,1000000000003710000000034573,100000000000031100000000014113

%N a(n) is the least prime that is the concatenation of two n-digit primes, and such that the concatenation of the same primes in the other order is also prime or 0 if no such prime exists.

%C Conjecture: a(n) > 0 and for n > 1 the first n digits of a(n) = A003617(n). - _Chai Wah Wu_, Jan 13 2021

%H Robert Israel, <a href="/A340539/b340539.txt">Table of n, a(n) for n = 1..171</a>

%e For n=4, 1009, 1789, 10091789 and 17891009 are all prime.

%p f:= proc(d) local P,a,b;

%p a:= prevprime(10^(d-1));

%p do

%p a:= nextprime(a);

%p if a > 10^d then return FAIL fi;

%p b:= prevprime(10^(d-1));

%p do

%p b:= nextprime(b);

%p if b > 10^d then break fi;

%p if isprime(10^d*a+b) and isprime(10^d*b+a) then return 10^d*a+b fi;

%p od od:

%p FAIL

%p end proc:

%p f(1):= 37:

%p map(f, [$1..20]);

%Y Cf. A003617, A340487.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 10 2021