Why is JD 2451545.0 = January 1, 2000, Noon instead of JD 2451558.0? I know that JD0.0 is Jan. 1st 4713 BC at Noon, a year in the Julian calendar is 365.25 days and that the number after 'JD' is the number of days so...

I want to calculate the number of days between Jan1.2000AD and Jan1.4713BC and I do

$$ \text{# of years} = 4712+2000=6712 \text{ years (skipping the year 0)} $$
$$ \text{# of days} = 6712 \cdot 365.25 =2451558 $$

So I think it should be JD2451558. An extra 13 days. What's going on here? I thought maybe the length of a year in the Julian calendar is $2451545/6712=365.2480632\text{days}$ but I can't find anything to support that.

I imagine that people would have questioned whoever proposed J2000 as JD2451545.0 and got a satisfying answer but I can't find one! Help
This Wikipedia article states (correctly) that


  "The Julian Day Number (JDN) is the integer assigned to a whole solar
  day in the Julian day count starting from noon Greenwich Mean Time,
  with Julian day number 0 assigned to the day starting at noon on
  January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC,
  in the proleptic Gregorian calendar)"


The Julian year consists of 365.25 days while a Gregorian year consists of 365.2425 days.  

Since the introduction of the Gregorian calendar, the difference between Gregorian and Julian calendar dates has increased by three days every four centuries (all date ranges are inclusive).  In addition, 10 days were added to the Julian calendar to obtain the Gregorian calendar at the time of the calendar reform. The current difference between the Gregorian and Julian calendar dates is 13 days: 14 September 2016 Gregorian date is 1 September 2016 (Julian date).

This should explain the extra 13 days in your calculations.