A249376 Prime numbers Q such that the concatenation Q,3,Q is prime.

11, 13, 17, 19, 37, 41, 53, 59, 79, 83, 97, 109, 127, 137, 151, 167, 179, 197, 211, 223, 241, 263, 283, 349, 367, 409, 461, 463, 503, 509, 523, 577, 587, 593, 599, 643, 739, 769, 787, 809, 827, 829, 853, 967, 977, 1049

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

333 is composite, 535 is composite, 737 is composite, 11311 is prime so a(1)=11.

Prog

(PFGW & SCRIPT), the pre10.txt file with the first 10000000 prime numbers.
SCRIPT
DIM i, 0
DIM j
DIM k
DIM n, 1
OPENFILEOUT myf, a(n).txt
OPENFILEIN maf, pre10.txt
GETNEXT j, maf
LABEL loop1
GETNEXT j, maf
IF j>10^n THEN SET n, n+1
SET k, j*10^(n+1)+3*10^n+j
PRP k
IF ISPRP THEN GOTO w
GOTO loop1
LABEL w
SET i, i+1
WRITE myf, j
IF i>9999 THEN END
GOTO loop1
(PARI) lista(nn) = {forprime(p=1, nn, if (isprime(eval(concat(concat(Str(p), 3), Str(p)))), print1(p, ", ")); ); } \\ Michel Marcus, Oct 27 2014
(Magma) [p: p in PrimesUpTo(3000) | IsPrime(Seqint(Intseq(p) cat [3] cat Intseq(p)))]; // Vincenzo Librandi, Oct 27 2014
(Python)
from sympy import isprime, primerange
def ok(p): s = str(p); return isprime(int(s + "3" + s))
def aupton(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupton(1050)) # Michael S. Branicky, Nov 13 2021

Crossrefs

Cf. similar sequences listed in A249374.

Sequence in context: A164329 A159236 A215417 * A068155 A271367 A226217

Adjacent sequences: A249373 A249374 A249375 * A249377 A249378 A249379

Keyword

nonn,base

Author

Pierre CAMI, Oct 27 2014

Status

approved