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

7810223, 19579907, 909001523, 984960937, 78406036607, 90124536947, 99020400307, 190002706337, 393086079907, 500708906197, 509000702017, 600180367883, 780430098443, 3534900290107, 5046024021013, 6006006800743, 6009000432797, 9001924501223, 12090900340283

Offset

1,1

Comments

These prime numbers are both:

- 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).

- 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.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..9175 (all terms with <= 29 digits)

Prog

(Python)
from sympy import isprime, primerange
def is_digitally_delicate(p):
    s = str(p)
    for i in range(len(s)):
        for d in "0123456789":
            if d != s[i] and not (i == int(d) == 0):
                if isprime(int(s[:i] + d + s[i+1:])): return False
    return True
def A033664gen(maxdigits):
    yield from [2, 3, 5, 7]
    primestrs, digits, d = ["2", "3", "5", "7"], "0123456789", 1
    while len(primestrs) > 0 and d < maxdigits:
        cands = (d+p for p in primestrs for d in "0123456789")
        primestrs = [c for c in cands if c[0] == "0" or isprime(int(c))]
        yield from sorted(map(int, (p for p in primestrs if p[0] != "0")))
        d += 1
def afind(maxdigits):
    for p in A033664gen(maxdigits):
        if is_digitally_delicate(p): print(p, end=", ")
afind(12) # Michael S. Branicky, Sep 01 2021

Crossrefs

Cf. A158124, A033664.

Sequence in context: A124416 A320516 A319809 * A214194 A205657 A206186

Adjacent sequences: A347421 A347422 A347423 * A347425 A347426 A347427

Keyword

nonn,base

Author

Marc Morgenegg, Sep 01 2021

Extensions

a(3)-a(4) from Amiram Eldar, Sep 01 2021

a(5)-a(19) from Michael S. Branicky, Sep 01 2021

Status

approved