A347864 Left- or right-truncatable primes, restricted to one consecutive zero.

2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, 113, 131, 137, 139, 167, 173, 179, 197, 223, 229, 233, 239, 271, 283, 293, 307, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 431, 433, 439, 443, 467, 479, 503

Offset: 1

Author

Timothy Smith, Jan 25 2022

Keywords

• nonn
• fini

Comments

There are 16484138 primes in this list, in total. The largest one has 60 digits and there is only one of that length.

Crossrefs

Left- or right-truncatable primes, excluding all 0s: A137812.

The number of primes of length n following these rules: A346662.

Programs

Python

from sympy import isprime
route = set({})
nums = [i*(10**j) for i in range(1, 10) for j in range(2)]
def addnum(a):
    global route
    for j in nums:
        b = int("{}{}".format(a, j))
        if isprime(b):
            if b not in route:
                route.add(b)
                addnum(b)
    for j in nums:
        b = int("{}{}".format(j, a))
        if isprime(b):
            if b not in route:
                route.add(b)
                addnum(b)
def run():
    for i in nums:
        if isprime(i):
            addnum(i)