A249377 Prime numbers Q such that the concatenation Q,4,Q is prime.

11, 17, 29, 53, 71, 107, 113, 179, 239, 263, 293, 317, 347, 401, 419, 503, 557, 569, 641, 659, 809, 857, 863, 941, 953, 983, 1049, 1103, 1277, 1301, 1319, 1439, 1487, 1553, 1613, 1667, 1733, 1877, 1889, 1901, 1907, 1949, 2243, 2381, 2447, 2477, 2687, 2693

Offset

1,1

Links

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

Example

343 is composite, 545 is composite, 747 is composite, 11411 is prime so a(1)=11.

Mathematica

Select[Prime[Range[300]], PrimeQ[FromDigits[Join[IntegerDigits[#], {4}, IntegerDigits[ #]]]]&] (* Harvey P. Dale, Aug 01 2016 *)

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)+4*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), 4), Str(p)))), print1(p, ", ")); ); } \\ Michel Marcus, Oct 27 2014
(Magma) [p: p in PrimesUpTo(3000) | IsPrime(Seqint(Intseq(p) cat [4] cat Intseq(p)))]; // Vincenzo Librandi, Oct 27 2014
(Python)
from sympy import isprime, primerange
def ok(p): s = str(p); return isprime(int(s + "4" + s))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(2700)) # Michael S. Branicky, Nov 17 2021

Crossrefs

Cf. similar sequences listed in A249374.

Sequence in context: A060213 A234098 A153502 * A211486 A208573 A142718

Adjacent sequences: A249374 A249375 A249376 * A249378 A249379 A249380

Keyword

nonn,base

Author

Pierre CAMI, Oct 27 2014

Status

approved