A125665 Numbers such that both the left half of the digits and right half of the digits form a prime.
2, 3, 5, 7, 22, 23, 25, 27, 32, 33, 35, 37, 52, 53, 55, 57, 72, 73, 75, 77, 202, 203, 205, 207, 212, 213, 215, 217, 222, 223, 225, 227, 232, 233, 235, 237, 242, 243, 245, 247, 252, 253, 255, 257, 262, 263, 265, 267, 272, 273, 275, 277, 282, 283, 285, 287, 292
Offset: 1
Examples
22 is the first number with this property having more than 1 digit.
Crossrefs
Cf. A125525.
Programs
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Mathematica
lhrhQ[n_]:=Module[{idn=IntegerDigits[n],len=Floor[IntegerLength[n]/2]}, And @@ PrimeQ[FromDigits/@{Take[idn,len],Take[idn,-len]}]]; Join[ {2,3,5,7}, Select[Range[300],lhrhQ]] (* Harvey P. Dale, Jul 05 2013 *) -
PARI
bothprime(n) = { local(x,ln,y,lp,rp); for(x=1,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",") ) ) }
Formula
The left half of an n-digit number is the first floor(n/2) digits. The right half of an n-digit number is the last floor(n/2) digits.
Comments