Perl, 33 bytes

Includes +1 for -p

Give the input number on STDIN

primecount.pl

#!/usr/bin/perl -p
$_=1x$_;$_=s%(?!(11+)\1+$)%%eg-2

Perl, 33 bytes

Includes +1 for -p

Give the input number on STDIN

primecount.pl

#!/usr/bin/perl -p
$_=1x$_;$_=s%(?!(11+)\1+$)%%eg-2

Gives the wrong result for 0 but that's OK, the op asked for support for positive integers only.