In the 60's Martin Gardner predicted that the millionth number of Pi was 5. At that time no one had a clue as to what it would be. 8 years later it was probed that Mr.Gardner was correct!
Any methods? Or was it just luck?
Owen

An interesting question! As far is known, calculating the millionth decimal digit of pi entails calculating the preceding 999999 digits. So if pi was not known to that degree of accuracy in the sixties, Gardner must have been guessing!

Astonishingly, the same is not true for base 16. It is possible to calculate the millionth hexadecimal digit of pi without calculating the preceding digits!

See David Bailey's homepage for further details.

Wow!

Jack Shalom

Thanks for the lin, when I have more time I shall read it in more detail!
owen

>Any methods? Or was it just luck?

Note that a book about Martin Gardner is available on-line, you can even download it for free.

http://www.g4g4.com/contentsmmpp.html

To sum, yes it was mere luck. In fact it was a hoax that turned out to be correct !

And for the millionth digit in decimal form, you have a "formula" using, uh, "only" the first 2 million prime numbers, in :

http://fabrice.bellard.free.fr/pi/pi_n2/pi_n2.html

An anecdote : you can see at the Palais de la Decouverte in Paris, France, a room with the 707th first digits of Pi circling the room. They are now correct, but until the 1950s, these figures were those computed by hand by W. Shanks in the 1870s after several years of work. Alas he was wrong after the 528th decimal !!