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

1,1

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

Links

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

Example

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]

Prog

(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", ") ) ) }

Crossrefs

Cf. A125523, A125524.

Sequence in context: A262098 A074491 A154385 * A019546 A104179 A096148

Adjacent sequences: A125522 A125523 A125524 * A125526 A125527 A125528

Keyword

base,easy,nonn

Author

Cino Hilliard, Jan 22 2007

Extensions

Offset changed to 1 by Zak Seidov, Feb 19 2015

Status

approved