A125590 Largest n-digit base-10 deletable prime.
7, 97, 997, 9973, 99929, 999907, 9999907, 99999307, 999996671, 9999996073, 99999966307, 999999908773, 9999999710639, 99999999697769, 999999997160639, 9999999996977699, 99999999980803477, 999999999961861807, 9999999999961861807, 99999999999807429133
Offset: 1
Examples
99929 -> 9929 -> 929 -> 29 -> 2.
References
- C. Caldwell, Truncatable primes, J. Recreational Math., 19:1 (1987) 30-33. [Discusses left truncatable primes, right truncatable primes and deletable primes.]
Links
- I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
- C. Caldwell, Deletable primes
- Prime Curios, A 300-digit example
- Carlos Rivera, Puzzle 138: Deletable Primes, Prime Puzzles and Problems Connection. [Includes a 500-digit example]
- Index entries for sequences related to truncatable primes
Programs
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Mathematica
b = 10; a = {7}; d = {2, 3, 5, 7}; For[n = 2, n <= 5, n++, p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &]; For[i = 1, i <= Length[p], i++, c = IntegerDigits[p[[i]], b]; For[j = 1, j <= n, j++, t = Delete[c, j]; If[t[[1]] == 0, Continue[]]; If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]]; AppendTo[a, Last[d]]]; a (* Robert Price, Nov 13 2018 *) -
Python
from sympy import isprime, prevprime from functools import cache @cache def deletable_prime(n): if not isprime(n): return False if n < 10: return True s = str(n) si = (s[:i]+s[i+1:] for i in range(len(s))) return any(t[0] != '0' and deletable_prime(int(t)) for t in si) def a(n): p = prevprime(10**n) while not deletable_prime(p): p = prevprime(p) return p print([a(n) for n in range(1, 15)]) # Michael S. Branicky, Jan 13 2022
Extensions
a(6)-a(8) from Michael Kleber, Jan 08 2007
a(9)-a(16) from Joshua Zucker, May 11 2007
a(17)-a(20) from Michael S. Branicky, Jan 13 2022
Comments