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
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)
Programs
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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