A088784 Primes formed by concatenating a prime with the preceding prime.

53, 5347, 5953, 6761, 137131, 179173, 211199, 223211, 239233, 263257, 359353, 541523, 593587, 613607, 631619, 653647, 659653, 757751, 809797, 977971, 997991, 1009997, 11091103, 11291123, 12371231, 13991381, 15591553, 17831777, 19311913, 19791973, 19931987, 23092297

Offset: 1

Author

Chuck Seggelin (barkeep(AT)plasteredDragon.com), Oct 15 2003

Keywords

• base
• nonn

Examples

			a(2) = 5347 because 5347 is 53 (a prime) concatenated with 47 (the preceding prime).
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10300

Crossrefs

Cf. A088712.

Programs

Mathematica

concatpr[n_]:=FromDigits[Join[IntegerDigits[n],IntegerDigits[ NextPrime[ n,-1]]]]; Select[concatpr/@Prime[Range[400]],PrimeQ] (* Harvey P. Dale, May 12 2011 *)

PARI

for(n=1,10^3,p=prime(n); q=concat(Str(p),Str(precprime(p-1))); if(isprime(eval(q)), print1(q,", "))) \\ Derek Orr, Aug 14 2014

Python

from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p, pstr = 2, "2"
    while True:
        q = nextprime(p)
        qstr = str(q)
        t = int(qstr + pstr)
        if isprime(t):
            yield t
        p, pstr = q, qstr
print(list(islice(agen(), 32))) # Michael S. Branicky, Jan 05 2022

Extensions

Terms a(30), a(31) and a(32) added by K. D. Bajpai, Aug 14 2014