A055521 Restricted left truncatable (Henry VIII) primes.

773, 3373, 3947, 4643, 5113, 6397, 6967, 7937, 15647, 16823, 24373, 33547, 34337, 37643, 56983, 57853, 59743, 62383, 63347, 63617, 69337, 72467, 72617, 75653, 76367, 87643, 92683, 97883, 98317, 121997, 124337, 163853, 213613, 236653

Offset

1,1

Comments

There are 1440 such primes, the largest being 357686312646216567629137.

Left-truncatable primes (A024785) which have at least two digits and are not the end of a larger left-truncatable prime. - Jens Kruse Andersen, Jul 29 2014

References

Kahan, S. and Weintraub, S. "Left Truncatable Primes." J. Recr. Math. 29, 254-264, 1998.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..1440 (complete sequence)

I. O. Angell, and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.

James Grime and Brady Haran, 357686312646216567629137, Numberphile video (2018)

Eric Weisstein's World of Mathematics, Truncatable Prime

Index entries for sequences related to truncatable primes

Example

773 is in the sequence since 773, 73, 3 are primes, while no digit 1..9 gives a prime if placed before 773. 13 is not in the sequence since for example 113 is prime. 2 and 5 are disqualified for only having one digit. - Jens Kruse Andersen, Jul 29 2014

Prog

(Python)
from sympy import isprime, primerange
def afull():
    alst, prime_strs, an, digits = [], ["2", "3", "5", "7"], 0, 1
    while len(prime_strs) > 0:
        new_prime_strs = set()
        for p in prime_strs:
            can_extend = False
            for d in "123456789":
                c = d + p
                if isprime(int(c)):
                    can_extend = True
                    new_prime_strs.add(c)
            if digits > 1 and not can_extend:
                alst.append(int(p))
        prime_strs = new_prime_strs
        digits += 1
    return sorted(alst)
print(afull()) # Michael S. Branicky, Dec 11 2022

Crossrefs

Cf. A024785.

Sequence in context: A133963 A133964 A033919 * A060825 A255156 A365597

Adjacent sequences: A055518 A055519 A055520 * A055522 A055523 A055524

Keyword

nonn,base,fini,full

Author

Eric W. Weisstein

Status

approved