A125664 Numbers such that the right half of the digits form a prime and the left half do not.

12, 13, 15, 17, 42, 43, 45, 47, 62, 63, 65, 67, 82, 83, 85, 87, 92, 93, 95, 97, 102, 103, 105, 107, 112, 113, 115, 117, 122, 123, 125, 127, 132, 133, 135, 137, 142, 143, 145, 147, 152, 153, 155, 157, 162, 163, 165, 167, 172, 173, 175, 177, 182, 183, 185, 187

Offset: 1

Author

Cino Hilliard, Jan 29 2007

Keywords

• base
• easy
• nonn

Comments

If the number of digits in the number is odd > 1, then the middle digit is ignored.

Examples

			12 is the first number with this property.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125524.

Programs

PARI

rightprime(n) = { local(x,ln,y,lp,rp); for(x=1,n, y=Str(x); if(x > 9, ln=floor(length(y)/2), ln=1); lp = eval(left(y,ln)); rp = eval(right(y,ln)); if(!isprime(lp)&& isprime(rp),print1(x",") ) ) }

Python

from sympy import isprime
def ok(n):
    if n < 10: return False
    s = str(n)
    m = len(s)//2
    return isprime(int(s[-m:])) and not isprime(int(s[:m]))
print([k for k in range(188) if ok(k)]) # Michael S. Branicky, Dec 13 2021

Formula

The left half of an n-digit number is the first floor(n/2) digits. The right half of an n-digit number is the last floor(n/2) digits.