A247098 Smallest prime p that generates n different primes if it is inserted into p itself.

2, 109, 131, 10289, 12197, 1227797, 101636629, 118561139, 10596073217, 89466662147, 37898818253

Offset: 0

Author

Paolo P. Lava, Nov 18 2014

Keywords

• nonn
• base
• more

Comments

a(8) > 10^9.

The concatenation of p with p will not result in a prime as the result is divisible by 10^k+1, where k is the number of digits in p. - Chai Wah Wu, Jun 25 2019

Examples

			a(0) = 2 is prime but concat(2,2) = 22 is not.
a(1) = 109 is prime and also concat(1,109,09) = 110909.
a(2) = 131 is prime. Again, concat(13,131,1) = 131311 is prime and also concat(1,131,31) = 113131.
a(5) = 1227797 and the five primes that are generated are: 12277912277977, 12271227797797, 12212277977797, 12122779727797, 11227797227797.
		

Crossrefs

Cf. A250311, A250312.

Programs

Maple

P:=proc(q) local a,b,i,j,k,n,t: print(2); for j from 1 to q do n:=2:
for k from 1 to q do n:=nextprime(n): b:=length(n): t:=0:
for i from 1 to b-1 do if isprime((trunc(n/10^i)*10^b+n)*10^i+(n mod 10^i))
then t:=t+1; fi; od;  if t=j then print(n); break; fi; od; od; end: P(10^9);

Extensions

a(8)-a(10) from Chai Wah Wu, Jul 01 2019