|
|
A345529
|
|
Primes that yield a prime when any single digit is replaced by its 10's complement.
|
|
0
|
|
|
3, 5, 7, 17, 47, 71, 107, 223, 401, 823, 827, 857, 883, 2087, 2089, 2539, 3253, 4007, 5051, 5059, 5503, 5507, 7541, 8447, 10247, 12401, 18041, 25303, 33529, 33589, 35533, 40427, 44171, 45557, 53503, 53653, 53899, 54401, 55001, 55009, 55333, 55817, 57077, 71147, 81017, 82003, 93553
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Digital complement of a digit d is 10-d if d > 0, 0 otherwise.
|
|
LINKS
|
|
|
EXAMPLE
|
71147 is a term since 31147, 79147, 71947, 71167 and 71143 are all primes.
|
|
MATHEMATICA
|
q[n_] := PrimeQ[n] && Module[{d = IntegerDigits[n]}, And @@ PrimeQ[Table[ FromDigits[ReplacePart[d, i -> If[d[[i]] == 0, d[[i]], 10 - d[[i]]]]], {i, 1, Length[d]}]]]; Select[Range[10^5], q] (* Amiram Eldar, Jul 06 2021 *)
|
|
PROG
|
(Python)
from sympy import isprime, primerange
def comp(d, i): return d[:i] + str((10-int(d[i]))%10) + d[i+1:]
def ok(p):
d = str(p)
return all(isprime(int(comp(d, i))) for i in range(len(d)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|