A340539 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.

37, 1123, 101107, 10091789, 1000710709, 100003100363, 10000031000303, 1000001910002521, 100000007100010321, 10000000071000000349, 1000000001910000000799, 100000000003100000009939, 10000000000391000000012387, 1000000000003710000000034573, 100000000000031100000000014113

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 10 2021

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..171

Crossrefs

Cf. A003617, A340487.

Programs

Maple

f:= proc(d) local P,a,b;
  a:= prevprime(10^(d-1));
  do
    a:= nextprime(a);
    if a > 10^d then return FAIL fi;
    b:= prevprime(10^(d-1));
    do
      b:= nextprime(b);
      if b > 10^d then break fi;
      if isprime(10^d*a+b) and isprime(10^d*b+a) then return 10^d*a+b fi;
  od od:
  FAIL
end proc:
f(1):= 37:
map(f, [$1..20]);