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

Author

Eric W. Weisstein

Keywords

• nonn
• base
• fini
• full

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

Examples

			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
		

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

Crossrefs

Cf. A024785.

Programs

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