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

Author

Marc Morgenegg, Sep 01 2021

Keywords

• nonn
• base

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)

Crossrefs

Cf. A158124, A033664.

Programs

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

Extensions

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

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