A337508 Primes such that neither the left half nor the right half of the prime is prime.

11, 19, 41, 61, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491, 499, 601, 619, 631, 641, 659, 661, 691, 809, 811, 821, 829, 839, 859, 881, 911, 919, 929, 941, 971, 991, 1009, 1021, 1033, 1039, 1049, 1051

Offset: 1

Author

Iain Fox, Aug 30 2020

Keywords

• nonn
• easy
• base

Comments

For n > 9, the center digit is not considered when making the calculation. For a prime number to be in this sequence, both the substring to the left of the center and the substring to the right of the center must be nonprime.

If a number appears in this sequence, it will not appear in A125523, A125524, or A125525.

A000040 is the union of this sequence, A125523, A125524, and A125525.

Examples

			479 is prime. The left part of (4)79 is not prime. The right part of 47(9) is not prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A125523, A125524, A125525.

Programs

Maple

q:= n-> isprime(n) and (s-> (h-> not ormap(x-> isprime(parse(x)),
        [s[1..h], s[-h..-1]]))(iquo(length(s), 2)))(""||n):
select(q, [$11..2000])[];  # Alois P. Heinz, Sep 14 2020

Mathematica

lhrhQ[p_]:=Module[{idp=IntegerDigits[p],c},c=Floor[Length[idp]/2];AllTrue[ {FromDigits[ Take[idp,c]],FromDigits[Take[idp,-c]]},!PrimeQ[#]&]]; Select[Prime[Range[5,200]],lhrhQ] (* Harvey P. Dale, Aug 09 2023 *)

PARI

lista(nn) = forprime(p=11, nn, my(l=#Str(p), e=floor(l/2), left=floor(p/10^(e+l%2)), right=p-floor(p/10^e)*10^e); if(!isprime(left) && !isprime(right), print1(p, ", ")))

Python

from sympy import nextprime, isprime
A337508_list, p = [], 11
while p < 10**6:
    s = str(p)
    l = len(s)//2
    if not (isprime(int(s[:l])) or isprime(int(s[-l:]))):
        A337508_list.append(p)
    p = nextprime(p) # Chai Wah Wu, Sep 14 2020