A258214 Primes formed by concatenating p^2 with q, where p, q are consecutive primes.

43, 257, 12113, 84131, 96137, 168143, 372167, 32041181, 120409349, 139129379, 292681547, 410881643, 516961727, 528529733, 863041937, 966289991, 10629611033, 10670891039, 11902811093, 16307291279, 21112091459, 25058891597, 29618411723, 31933691789, 35006411873

Offset: 1

Author

K. D. Bajpai, May 23 2015

Keywords

• nonn
• base

Comments

All the terms in this sequence, except a(1), are congruent to 2 (mod 3).

Examples

			a(2) = 257 is prime formed by concatenation of (5^2) = 25 with 7.
a(3) = 12113 is prime formed by concatenation of (11^2) = 121 with 13.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A030461, A030469.

Programs

Magma

[m: n in [1..300] | IsPrime(m) where m is Seqint(Intseq(NthPrime(n+1)) cat Intseq(NthPrime(n)^2))]; // Vincenzo Librandi, May 24 2015

Mathematica

Select[Table[p = Prime[n]; FromDigits[Join[Flatten[ IntegerDigits[{p^2, NextPrime[p]}]]]], {n, 500}], PrimeQ]
Select[#[[1]]^2*10^IntegerLength[#[[2]]]+#[[2]]&/@Partition[Prime[ Range[ 300]],2,1],PrimeQ] (* Harvey P. Dale, Dec 05 2016 *)

PARI

forprime(p = 1,5000, k=eval(concat( Str(p^2), Str(nextprime(p+1)) )); if(isprime(k), print1(k,", ")))