A309935 Primes p such that the base-10 concatenation (p+1)||p is prime.

3, 23, 41, 101, 107, 113, 179, 191, 197, 263, 269, 281, 293, 311, 353, 383, 389, 419, 443, 491, 521, 569, 659, 683, 701, 761, 773, 809, 821, 839, 881, 887, 911, 947, 1109, 1217, 1223, 1229, 1433, 1481, 1499, 1559, 1667, 1697, 1811, 1901, 1973, 2069, 2087, 2099, 2111, 2129

Offset: 1

Author

Robert Israel, Aug 23 2019

Keywords

• nonn
• base

Examples

			a(3) = 41 is in the sequence because 41 and 4241 are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Magma

[p:p in PrimesUpTo(2200)| IsPrime(Seqint(Intseq(p) cat Intseq(p+1)))]; // Marius A. Burtea, Aug 23 2019

Maple

select(t -> isprime(t) and isprime(10^(1+ilog10(t))*(t+1)+t), [$1..20000]);

Mathematica

Select[Prime[Range[350]],PrimeQ[(#+1)10^IntegerLength[#]+#]&] (* Harvey P. Dale, May 07 2022 *)

PARI

isok(k) = isprime(k) && isprime(eval(Str(k+1, k))); \\ Jinyuan Wang, Aug 26 2019