At 1st glance, it sounds like someone may have tried to make an analogy between the letters of the Torah and the 6000 years that this world will exist including the days of the Messiah.
A Torah actually contains 304,805 letters. But like is emphasized in kabbalistic and chassidic teachings, letters are defined in 2 ways.
Written letters are defined by positive space/boundary. Engraved letters are defined by negative space/boundary.
If one considers the analogy in the physical universe of matter (what we see and detect) and dark matter (the aspect of matter which we generally don't see or detect and which comprises according to current theories the majority of the universe), the idea isn't so difficult to comprehend. Dark matter would equate with the space around each letter in a Sefer Torah. For the Sefer Torah to be valid, each letter must have that clear space around it. When considering the entire klaf of the Sefer Torah (the surface of skin written upon which is also empty space) the dark matter is far greater than the matter (the ink).
So absolute letter definition has both definition aspects resulting in the concept that the Torah contains (approximately) 600,000 letters. Doubling 304,805 results in exactly 609,610 letters.
Dividing by 100 to draw the analogy to exact years results in 6,096 years that this world will last.
This would then alter the calculations of how long a day in terms of G-d's years from Chapter 90:4 of Tehillim results in.
For in Your sight a thousand years are like yesterday that has passed, like a watch of the night.
The Messianic period begins before the end of the 6th day (actual Shabbat) following the halachic concept of when Shabbat should be brought in on Friday.
Doing the math, 6096 years divided by 6 days means a single day is 1,016 years exactly. Dividing by 24 hours in a day results in 42.333 years per halachic hour.
The earliest to take on Shabbat is Plag HaMinchah or 1.25 hours before actual night. 42.333 years times 1.25 results in 52.9 (53 years) before the 6,096 actual years that this world will exist, or the year 6,043 (which coincides to Plag HaMinchah of the sixth day) is the commencement of the Messianic period using that analogy with the actual number of letters of the Torah.
But just to emphasize, this is not the way this concept has been taught, neither by the Vilna Gaon, nor within the teachings of Chassidut.
The traditional teaching places Plag HaMinchah, meaning the beginning of the Messianic era, at the year 5750/51 or 1990/1991 on the secular calendar.
