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The 'proleptic Gregorian calendar' is produced by extending the Gregorian calendar to dates preceding its official introduction in 1582.
Most Maya scholars use the proleptic Gregorian calendar, especially when converting Long Count dates (first century BC to tenth century). It is also explicitly required for all dates before 1582 by ISO8601:2004 (4.3.2.1), if the partners to information exchange agree. However, neither astronomers nor non-Maya historians generally use it.
For these calendars we can distinguish two systems of numbering years BC. Bede and later historians did not use the Latin zero, ''nulla'', as a year, so the year preceding AD 1 is 1 BC. In this system the year 1 BC is a leap year (likewise in the proleptic Julian calendar). Mathematically, it is more convenient to include a year zero and represent earlier years as negative. This is the convention used in astronomical year numbering and in the international standard date system, ISO 8601. In these systems, the year 0 is a leap year.
Note that the Julian calendar was in actual use from AD 1 until 1582 or later (see From Julian to Gregorian), so historians and astronomers prefer to use the actual Julian calendar during that period. Likewise, the proleptic Julian calendar is used to specify dates before AD 1, the first common year that did not follow a quadrennial leap year (leap years between 45 BC and 1 BC were irregular, see Leap year error). But when seasonal dates are important, the proleptic Gregorian calendar is sometimes used, especially when discussing cultures that did not use the Julian calendar.
The proleptic Gregorian calendar is sometimes used in computer software to simplify the handling of older dates. For example, it is the calendar used by MySQL. [1]

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Difference between Julian and proleptic Gregorian calendar dates

Difference between Julian and proleptic Gregorian calendar dates

Before the introduction of the Gregorian calendar, the difference between Julian and proleptic Gregorian calendar dates has increased as follows:

Julian range	Proleptic Gregorian range	Difference
From 1 March 200 to 28 February 300	From 1 March 200 to 28 February 300	0 days
From 29 February 300 to 27 February 500	From 1 March 300 to 28 February 500	1 day
From 28 February 500 to 26 February 600	From 1 March 500 to 28 February 600	2 days
From 27 February 600 to 25 February 700	From 1 March 600 to 28 February 700	3 days
From 26 February 700 to 24 February 900	From 1 March 700 to 28 February 900	4 days
From 25 February 900 to 23 February 1000	From 1 March 900 to 28 February 1000	5 days
From 24 February 1000 to 22 February 1100	From 1 March 1000 to 28 February 1100	6 days
From 23 February 1100 to 21 February 1300	From 1 March 1100 to 28 February 1300	7 days
From 22 February 1300 to 20 February 1400	From 1 March 1300 to 28 February 1400	8 days
From 21 February 1400 to 19 February 1500	From 1 March 1400 to 28 February 1500	9 days
From 20 February 1500 to 4 October 1582	From 1 March 1500 to 14 October 1582	10 days