A082756 Larger of a pair of consecutive primes having only prime digits.

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

Offset: 1

Author

Amarnath Murthy, Apr 18 2003

Keywords

• base
• nonn

Examples

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

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A019546, A082755.

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[q]], {n, 1, 20000}]
Transpose[Select[Partition[Prime[Range[20000]],2,1],And@@PrimeQ[ Flatten[ IntegerDigits/@#]]&]] [[2]] (* Harvey P. Dale, Jul 19 2011 *)

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
print(list(islice(agen(), 40))) # Michael S. Branicky, Mar 11 2022

Extensions

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

a(38) and beyond from Michael S. Branicky, Mar 11 2022