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A125525 Centrist primes: primes such that both the right half and the left half of the prime are prime. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)