The first 10 digits are 3.1415926535 (rounds to 3.1415926536) and these are sufficient for all but the most rigorous calculations. There is a text file available at the related link that has the first billion (takes at least 35 seconds to load, but as long as 5 minutes). A character in an ASCII text file is one byte, so a trillion digits is a terabyte... no one has such a file available for download. A customized compression routine could easily get this down to a half-byte per digit, but that's still hundreds of gigabytes for a trillion digits.
The field size of this page cannot accommodate even the first 200,000 digits.
(There's no reason to try to find a repeating pattern, because there isn't one. Pi is an irrational number so will not repeat digits as in a fractional division. This also means it doesn't compress terribly well.)
NOTE: You can calculate the circumference of the observable universe to the accuracy of the diameter of a single atom with 34 digits of pi, so you probably don't need any more.
If you want them just because you're curious, there's a link in the Related Links section to the page of someone who has calculated pi to ten trillion digits. The file containing these is terabytes in size, so it's not available for download, but the program used to calculate them is so you can run it yourself if you've got a few months and a very large disk to spare.
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1.2411 trillion digits (1,241,100,000,000) digits of pi have been dicovered.
The decimal representation of pi, as of late 2011, is over 10 trillion (1013) digits.
The decimal representation of pi, as of late 2011, is over 10 trillion (1013) digits.
An infinite number. As of late 2011, over 10 trillion (1013) digits have been computed.
The first 55 digits of pi after the decimal point are: 3.1415926535897932384626433832795028841971693993751058209