A125524 Republican primes: primes such that the right half of the prime is prime and the left half is not.

13, 17, 43, 47, 67, 83, 97, 103, 107, 113, 127, 137, 157, 163, 167, 173, 193, 197, 433, 443, 457, 463, 467, 487, 607, 613, 617, 643, 647, 653, 673, 677, 683, 823, 827, 853, 857, 863, 877, 883, 887, 907, 937, 947, 953, 967, 977, 983, 997, 1013, 1019, 1031

Offset: 2

Author

Cino Hilliard, Jan 22 2007

Keywords

• base
• easy
• nonn

Comments

If the length of n is odd then the central number is not used in the calculation. So neither the left half nor the right half will contain the central digit. If the length of n is even, then all numbers are used.

Examples

			The right half of 13 is 3, which is prime. The left half is 1, which is not prime.
The right half of 113 is 3, which is prime. The left half is 1, which is not prime.
		

Links

• Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)

Crossrefs

Cf. A125523, A125525.

Programs

PARI

/* Political primes, republican case. */ rep(n) = { local(x,ln,y,lp,rp); forprime(x=2,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",") ) ) }