|
|
A082756
|
|
Larger of a pair of consecutive primes having only prime digits.
|
|
2
|
|
|
3, 5, 7, 227, 733, 3257, 3733, 5237, 5333, 7577, 7727, 7757, 22277, 23333, 25537, 27737, 32237, 32327, 32537, 35327, 35537, 37273, 37277, 52237, 52733, 53327, 53353, 53777, 55337, 72227, 72733, 75227, 75533, 75557, 222533, 222553, 222557, 223277, 223757, 225227
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
227 is a term as the previous prime 223 also has only prime digits.
|
|
MATHEMATICA
|
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 0; q = 1; pd = {1}; Do[p = q; pd = qd; q = NextPrim[p]; qd = Union[ Join[{2, 3, 5, 7}, IntegerDigits[q]]]; If[pd == qd == {2, 3, 5, 7}, Print[q]], {n, 1, 20000}]
Transpose[Select[Partition[Prime[Range[20000]], 2, 1], And@@PrimeQ[ Flatten[ IntegerDigits/@#]]&]] [[2]] (* Harvey P. Dale, Jul 19 2011 *)
|
|
PROG
|
(Python)
from sympy import nextprime, isprime
from itertools import count, islice, product
def onlypd(n): return set(str(n)) <= set("2357")
def agen():
yield from [3, 5, 7]
for digits in count(2):
for p in product("2357", repeat=digits-1):
for end in "37":
t = int("".join(p) + end)
if isprime(t):
t2 = nextprime(t)
if onlypd(t2):
yield t2
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|