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%I #16 May 26 2019 04:39:34
%S 13,17,43,47,67,83,97,103,107,113,127,137,157,163,167,173,193,197,433,
%T 443,457,463,467,487,607,613,617,643,647,653,673,677,683,823,827,853,
%U 857,863,877,883,887,907,937,947,953,967,977,983,997,1013,1019,1031
%N Republican primes: primes such that the right half of the prime is prime and the left half is not.
%C 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.
%H Tony Padilla and Brady Haran, <a href="https://www.youtube.com/watch?v=zk_Q9y_LNzg">The Most Evil Number</a>, Numberphile video (2018)
%e The right half of 13 is 3, which is prime. The left half is 1, which is not prime.
%e The right half of 113 is 3, which is prime. The left half is 1, which is not prime.
%o (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",") ) ) }
%Y Cf. A125523, A125525.
%K base,easy,nonn
%O 2,1
%A _Cino Hilliard_, Jan 22 2007
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