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A347424 Digitally delicate truncatable primes: every suffix is prime, changing any one decimal digit always produces a composite number, except the first to zero.

%I A347424 #27 Sep 05 2021 08:13:03
%S A347424 7810223,19579907,909001523,984960937,78406036607,90124536947,
%T A347424 99020400307,190002706337,393086079907,500708906197,509000702017,
%U A347424 600180367883,780430098443,3534900290107,5046024021013,6006006800743,6009000432797,9001924501223,12090900340283
%N A347424 Digitally delicate truncatable primes: every suffix is prime, changing any one decimal digit always produces a composite number, except the first to zero.
%C A347424 These prime numbers are both:
%C A347424 - digitally delicate primes (also called weakly prime numbers) A158124: changing any one decimal digit always produces a composite number, with restriction that first digit may not be changed to a 0 (that means no change of the number of significant digits from its original value).
%C A347424 - left-truncatable primes A033664:  every suffix is prime, means repeatedly deleting the most significant digit gives a prime at every step until a single-digit prime remains.
%H A347424 Michael S. Branicky, <a href="/A347424/b347424.txt">Table of n, a(n) for n = 1..9175</a> (all terms with <= 29 digits)
%o A347424 (Python)
%o A347424 from sympy import isprime, primerange
%o A347424 def is_digitally_delicate(p):
%o A347424     s = str(p)
%o A347424     for i in range(len(s)):
%o A347424         for d in "0123456789":
%o A347424             if d != s[i] and not (i == int(d) == 0):
%o A347424                 if isprime(int(s[:i] + d + s[i+1:])): return False
%o A347424     return True
%o A347424 def A033664gen(maxdigits):
%o A347424     yield from [2, 3, 5, 7]
%o A347424     primestrs, digits, d = ["2", "3", "5", "7"], "0123456789", 1
%o A347424     while len(primestrs) > 0 and d < maxdigits:
%o A347424         cands = (d+p for p in primestrs for d in "0123456789")
%o A347424         primestrs = [c for c in cands if c[0] == "0" or isprime(int(c))]
%o A347424         yield from sorted(map(int, (p for p in primestrs if p[0] != "0")))
%o A347424         d += 1
%o A347424 def afind(maxdigits):
%o A347424     for p in A033664gen(maxdigits):
%o A347424         if is_digitally_delicate(p): print(p, end=", ")
%o A347424 afind(12) # _Michael S. Branicky_, Sep 01 2021
%Y A347424 Cf. A158124, A033664.
%K A347424 nonn,base
%O A347424 1,1
%A A347424 _Marc Morgenegg_, Sep 01 2021
%E A347424 a(3)-a(4) from _Amiram Eldar_, Sep 01 2021
%E A347424 a(5)-a(19) from _Michael S. Branicky_, Sep 01 2021