A125525 Centrist primes: primes such that both the right half and the left half of the prime are prime.

2, 3, 5, 7, 23, 37, 53, 73, 223, 227, 233, 257, 263, 277, 283, 293, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 503, 523, 547, 557, 563, 577, 587, 593, 727, 733, 743, 757, 773, 787, 797, 1103, 1117, 1123, 1129, 1153, 1171, 1303, 1307, 1319, 1361, 1367

Offset: 1

Author

Cino Hilliard, Jan 22 2007

Keywords

• base
• easy
• nonn

Comments

If the length of n > 9 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. My guess is there are infinitely many of these numbers.

Number of n-digit terms for n=1..9: {4, 4, 33, 92, 1100, 3223, 37611, 130607, 1590017}. - Zak Seidov, Feb 19 2015

Examples

			The left half of 23 is 2 which is prime. The right half is 3 which is also prime so 23 is a centrist prime. [Corrected by _N. J. A. Sloane_, Jan 12 2019]
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125523, A125524.

Programs

PARI

left(str, n) = /* Get the left n characters from string str */ { my(v, tmp, x); v =""; tmp = Vec(str); ln=length(tmp); if(n > ln, n=ln); for(x=1, n, v=concat(v, tmp[x]); ); return(v) }
right(str, n) = /* Get the right n characters from string str.*/ { my(v, ln, s, x); v =""; tmp = Vec(str); ln=length(tmp); if(n > ln, n=ln); s = ln-n+1; for(x=s, ln, v=concat(v, tmp[x]); ); return(v) }
/* Political primes, Centrist case */ rep(n) = { my(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",") ) ) }

Extensions

Offset changed to 1 by Zak Seidov, Feb 19 2015