A082755 Smaller of a pair of consecutive primes having only prime digits.

2, 3, 5, 223, 727, 3253, 3727, 5233, 5323, 7573, 7723, 7753, 22273, 23327, 25523, 27733, 32233, 32323, 32533, 35323, 35533, 37253, 37273, 52223, 52727, 53323, 53327, 53773, 55333, 72223, 72727, 75223, 75527, 75553, 222527, 222533, 222553, 223273, 223753, 225223

Offset: 1

Author

Amarnath Murthy, Apr 18 2003

Keywords

• base
• nonn

Examples

			223 is a term as the next prime 227 also has only prime digits.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (Terms for n = 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A019546, A082756.

Programs

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[p]], {n, 1, 20000}]
Prime[#]&/@SequencePosition[Table[If[AllTrue[IntegerDigits[n],PrimeQ],1,0],{n,Prime[Range[20000]]}],{1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 31 2017 *)

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 [2, 3, 5]
    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) and onlypd(nextprime(t)):
                    yield t
print(list(islice(agen(), 40))) # Michael S. Branicky, Mar 11 2022

Extensions

Edited and extended by Robert G. Wilson v, Apr 22 2003