A068803 Smaller of two consecutive primes which have no common digits.

2, 3, 5, 7, 19, 29, 37, 47, 59, 79, 97, 397, 499, 599, 1999, 2999, 3989, 4999, 29989, 49999, 59999, 79999, 199999, 599999, 799999, 2999999, 4999999, 5999993, 19999999, 29999999, 59999999, 69999989, 99999989, 199999991, 699999953, 799999999, 5999999989, 6999999989

Offset: 1

Author

Amarnath Murthy, Mar 06 2002

Keywords

• base
• nonn

Comments

Is the sequence finite or infinite?

Except for 2, 3, 5, and 7, all such primes are of the form a*10^n-b with 1 <= a <= 8 and b mod 10 = 1, 3, 7 or 9. An example of a large pair is 10^101-203 and 10^101+3. The largest known pair of probable primes is 8*10^5002-6243 and 8*10^5002+14481. - Lewis Baxter, Mar 06 2023

Examples

			397 is a term as 397 and 401 are two consecutive primes with no common digits.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..804

Crossrefs

Cf. A076490.

Programs

Mathematica

First /@ Select[Partition[Prime[Range[10^6]], 2, 1], Intersection @@ IntegerDigits /@ # == {} &] (* Jayanta Basu, Aug 06 2013 *)

PARI

isok(p) = isprime(p) && (#setintersect(Set(digits(p)), Set(digits(nextprime(p+1)))) == 0); \\ Michel Marcus, Mar 27 2023

Python

from itertools import count, islice
from sympy import nextprime, prevprime
def agen(): # generator of terms
    yield from [2, 3, 5]
    for d in count(2):
        for b in range(10**(d-1), 10**d, 10**(d-1)):
            p, q = prevprime(b), nextprime(b)
            if set(str(p)) & set(str(q)) == set():
                yield p
print(list(islice(agen(), 40))) # Michael S. Branicky, May 09 2023

Extensions

More terms from Larry Soule (lsoule(AT)gmail.com), Jun 21 2006

a(36) and beyond from Michael S. Branicky, May 09 2023