When Does the Third Film "The Time Machine" (2002) Take Place?

"The Time Machine" is a science fiction film written by John Logan [adapting "The Time Machine" (1895) by H.G. Wells] that released March 8th, 2002. So when is "The Time Machine" set? 

It takes place in the year: 

802701 AD 

We know this because about a quarter through the story after one long trip into the future Columbia University professor Alexander Hartdegen pushes his time machine into a faster speed and the mechanical display reads "802701 Jul 16" as it finally slows to a stop. So it is July of 802701 AD. 

Additionally, there's a two-part prologue: 

-The first part includes a conversation with his friend David Philby that  "I think Mr. Einstein?", certainly referring to the real-world famous physicist Albert Einstein (1879-1955) so it must be after his birth in March of 1879 AD. Based on the incredulity with which Mr. Philby regards Prof. Hartdegen communicating with Einstein, we must assume it is before he became world famous with the publication of his Theory of Relativity the first part of which was made public on September 26th, 1905 AD. So it is certainly before late September of 1905 AD. 

More specifically, this first section ends with a relative time setting title card telling us it's "FOUR YEARS LATER" before the second part which we know occurs in 1903 AD. So it is 1899 AD. 

1,903 - 4 = 1,899. 

Specifically, as he later begins one of his first jumps the machine's rotating date display just begins to spin and it reads: "1899 Jan 18". He had just previously jumped backwards in time (possibly passing back-and-forth between January of 1899 AD and 1903 AD more than once off-screen). So presumably it is January of 1899 AD during the first part of the prologue. 

-The second part is the moment from which Alexander time-travels from for the first time ? and the VOX-114 artificial intelligence he interacts with in 2030 AD pins down his lifetime thus: "Alexander Hartdegen. 1869 to 1903." So it must be 1903 AD when he leaves home, first travels through time, and disappears from the public in-universe (diegetic) historical record. 

Then, in the middle of the movie, Alex makes his first trip beyond his own natural lifespan and as he stops the machine to look around its dials read: "02030 May 24" so it is May of 2030 AD. 

And just a few scenes afterward,  "2037" so it is 2037 AD. 

Finally, there is a very quick scene late in the narrative when Alex accidentally pushes much further into the future for a second time. This time when he pulls back the lever on his machine, it displays "635427810" so we know it is the far advanced year 635427810 AD.