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I need the number of exact days from October 23, 4004 B.C., but obviously it's a bit challenging, i.e. there were some days "disappeared" in the history, and things became a bit complicated.
How many days had it been from October 23, 4004 B.C. to September 17th, 2020?
This is a job for Julian day numbers.
Julian day is the continuous count of days since the beginning of the Julian Period and is used primarily by astronomers, and in software for easily calculating elapsed days between two events (e.g. food production date and sell by date).1
The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Universal time, with Julian day number 0 assigned to the day starting at noon on Monday, January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC, in the proleptic Gregorian calendar),23 a date at which three multi-year cycles started (which are: Indiction, Solar, and Lunar cycles) and which preceded any dates in recorded history.[a] For example, the Julian day number for the day starting at 12:00 UT (noon) on January 1, 2000, was 2 451 545.4
The Julian date (JD) of any instant is the Julian day number plus the fraction of a day since the preceding noon in Universal Time. Julian dates are expressed as a Julian day number with a decimal fraction added.[6] For example, the Julian Date for 00:30:00.0 UT January 1, 2013, is 2 456 293.520 833.[7] Expressed as a Julian date, right now it is 2459110.2399306. [refresh]
You want the number of days since October 23, 4004 B.C.
Nobody counted time as so many years or days until January 1, AD 1 back in 4004 BC. As far as I know the calendars which count years BC (or BCE) are the Julian and the Gregorian calendars, created millenia after 4004 BC. Therefore a date given as 4004 BC must be in the proleptic version of one of those calendars.
The adjective proleptic is defined as:
Of a calendar, extrapolated to dates prior to its first adoption; of those used to adjust to or from the Julian calendar or Gregorian calendar.
https://en.wiktionary.org/wiki/proleptic#:~:text=proleptic%20(comparative%20more%20proleptic%2C%20superlative,date%20that%20is%20too%20early.[5]
And I note that October 23, 4004 BC in the proleptic Julian calendar would be a different date than October 23, 4004 BC in the proleptic Gregorian clanedar.
The current Julian date is given as: 2459110.23958.
https://en.wikipedia.org/wiki/Julian_day#Variants[2]
Thus there is a fair chance that it will still be Julian day 2459110 when you read this. That is September 17, 2020, or Julian day 2,459,110.
You seem to be asking about Archbishop Ussher's date for the Creation, 23 October 4004 BC. His date of 4004 BC for the Creation is hardly the only date which has been proposed.
In 1738, Alphonse Des Vignoles [fr] said he had collected over 200 different estimates, ranging from 3483 BC to 6984 BC.
https://en.wikipedia.org/wiki/Dating_creation#Other_biblical_estimations[4]
Anyway, this online calculator says that October 23, 4004 BC was Julian date 259258.29721.
https://www.onlineconversion.com/julian_date.htm[3]
It doesn't specify whether 259258 equals October 23, 4004 BC in the proleptic Julian or Gregorian calendar.
2,459,110 minus 259,258 is 2,199,852 days. So I have found one of the two possible answers to your question.
[5]: https://en.wiktionary.org/wiki/proleptic#:~:text=proleptic%20(comparative%20more%20proleptic%2C%20superlative,date%20that%20is%20too%20early.
Days and years are based on two natural phenomena that are both completely disjoint and actually have varying jittering periods. So there's really no one answer to this.
Add in the fact that nobody was using the Gregorian Calendar or the Julian Calendar, or anything like either of them way back then, and in a lot of ways this isn't an answerable question.
Or to put it another way, in true Douglass Adams fashion, if you write a computer program that gives you an exact answer, you then would probably then need to write another one to explain to you what the actual question was.
For example, for the website used to give an exact number in another answer, we see this clarification:
The Gregorian calendar is used for dates on and after October 15, 1582 A.D. and the Julian calendar is used before October 4, 1582.
However, that "Julian" calendar had all sorts of special exceptions in it. For instance, there was one Julian year that lasted 446 days. After Julius' death, the leap day scheme was tweaked too. Without applying those same tweaks backwards, and adding some more of our own invention, the Julian calendar's year will slide significantly from the actual solar year by 4004 BCE. Did the website account for any of that? It didn't say. Is a Julian BCE date what you wanted? You didn't say.
This online calculator says 2,199,852 days. It says that the "Gregorian calendar is used for dates on and after October 15, 1582 A.D. and the Julian calendar is used before October 4, 1582". There may be alternative calculators available online if you search around.
Obviously nobody in 4004 BC would have said or written "4004 more years until the nominal date of the Birth of Christ." And Jesus was almost certainly not born in the night of December 25th, 1 AD. So a date like 4004 BC is only meaningful in hindsight.
The BC dates are used by historians who want to place events in ancient cultures into a timeline. They puzzle and argue which year BC the "year 1 of the reign of king Whoever" represents, and from time to time there are new puzzle pieces to shift things around.
A different kind of BC is used for astronomy, with a year 0 to simplify calculations.
Your question of "disappearing days" only makes sense for the count from 1 AD to today. Pope Gregor attempted to compensate for systematic errors (spacing of leap years) with his 1582 calendar reform. This would not have compensated for "disappeared" or "invented" years, however.
There is a conspiracy theory going around that some three centuries were invented by later chroniclers. There is overwhelming evidence that this conspiracy theory is wrong, not least by dated reports of astronomical events in ancient times and by the consistency of timelines in different civilizations.
So there are two questions to answer:
How many days between October 23, 4004 BC and January 1, 1 AD? Should be simple math.
How many days from January 1, 1 AD to today? Possibly a matter of faith.
70 days from October 23, 4004 BC to January 1, 4003 BC.
4003 years from January 1, 4003 BC to January 1, 1 AD. From these, 1000-40+8 = 968 were leap years. So 1,462,063 days.
2019 years from January 1, 1 AD to January 1, 2020 AD. Of these, 504-20+5 = 489 were leap days. So 737,424 days.
261 days from January 1, 2020 AD to today.
2,199,818 days, but that number is not really meaningful because it adds apples to oranges.
