

A119680


Prime numbers obtained by inserting a 0 between each pair of adjacent digits of a prime number > 10.


1



101, 103, 107, 109, 307, 401, 503, 509, 601, 607, 701, 709, 809, 907, 10007, 10009, 10103, 10301, 10501, 10607, 10709, 10903, 10909, 20101, 20507, 20707, 20903, 30103, 30307, 30509, 30703, 30803, 30809, 40009, 40507, 40709, 50707, 50909, 60103, 60107, 60509
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OFFSET

1,1


COMMENTS

See A159236 for the original prime numbers.
The least prime numbers > 10 remaining prime during exactly k iterations of the operation of inserting a 0 between each pair of adjacent digits are, for small values of k:
k prime
 
0 23
1 11
2 19
3 17
4 220333
5 8677267
(End)


LINKS



EXAMPLE

The first four terms arise from 11 > 101, 13 > 103, 17 > 107, 19 > 109.
23 > 203 is not prime, so 203 is not a term.


MATHEMATICA

a = Table[Table[Mod[Floor[Prime[m]/10^n], 10], {n, 4, 0, 1}], {m, 5, 200}]; Dimensions[a] b = Table[Sum[(If[Mod[n  1, 2] == 0, a[[m, 1 + Floor[(n  1)/2]]], 0])*10^(9  n), {n, 1, 9}], {m, 1, 195}]; c = Flatten[Table[If[PrimeQ[b[[m]]], b[[m]], {}], {m, 1, 195}]]


PROG

(PARI) forprime (p=10, 599, if (isprime(pp=fromdigits(digits(p), 100)), print1 (pp ", "))) \\ Rémy Sigrist, Oct 08 2017
(Python)
from itertools import count, islice
from sympy import isprime, nextprime
def ok(n):
return n > 10 and isprime(n) and isprime(int("0".join(list(str(n)))))
def agen():
p = 11
while True:
t = int("0".join(list(str(p))))
if isprime(t): yield t
p = nextprime(p)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



