A340487 a(n) is the least prime that is the concatenation of two n-digit primes, or 0 if there are none.

23, 1117, 101107, 10091021, 1000710181, 100003100129, 10000031000171, 1000001910000349, 100000007100000541, 10000000071000000349, 1000000001910000000319, 100000000003100000000063, 10000000000391000000000903, 1000000000003710000000000259, 100000000000031100000000000403

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

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

Examples

			a(3) = 101107 is prime and the concatenation of the two 3-digit primes 101 and 107.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..500 (n = 1..380 from Robert Israel)

Crossrefs

Cf. A003617.

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) then return 10^d*a+b fi;
  od od:
  FAIL
end proc:
f(1):= 23:
map(f, [$1..20]);