Pi Digits 3.14159…

The decimals of Pi refer to the digits following the decimal point in the decimal representation of the number Pi (π). Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. Its approximate value is 3.14159…, but its decimals are infinite and not periodic.

It is even conjectured that Pi is a universe number, that is to say a number whose decimals contain any finite series of digits.

To find a pattern of digits among the decimals of Pi, there is no quick formula to access a specific decimal (in base 10), the most obvious way is to calculate the decimals and iterate through them in order .

Consequently, it is not possible to predict the position of a digit or a number in the circle constant π.

Pour calculer le N-ième chiffre de Pi, il existe la formule de Bellard, qui permet de calculer la n-ième décimale de Pi en base 2 (ou 4, 8 ou 16).

For base 10, the only way is to calculate the first N decimals. dCode has already done this job, use the form to find the digit in position N.

There are an infinite number of decimal places in the number Pi (it is irrational and non periodic). Computers calculate new ones daily. dCode knows the pi decimals until 1000000 (one million digits of pi).

A number in which all other numbers can be found is called a rich number. Today it is not mathematically proven that Pi is a rich/disjunctive number.

If dCode does not find a number or a date, it is probably that it is beyond the first 1 million decimals.

Records are constantly improving, but the latest results are:

World records use the formula of the Chudnovsky brothers $$ \frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}} $$

More generally, Spigot's algorithms allow numbers to be calculated sequentially, thus increasing the precision at each step of the algorithm.

To calculate the first decimals, Leibniz's formula for Pi is quickly implemented in pseudocode:// pseudo-code
function generatePi() {
piApproximation = 0.0
sign = 1
for (i = 0 ; i < 1000000 ; i++) {
piApproximation += sign / (2 * i + 1)
sign = -sign
}
piApproximation = 4 * piApproximation
return piApproximation
}

On the other hand the convergence is very slow, 300 iterations are necessary for only 2 decimals.

The 100 tiillion first decimal places of pi are available on a Google server here but for information, in order to download them, provide a hard drive of 82 Tb (82,000 Giga-bytes)

The number Pi has an infinite number of digits after the decimal point. Talking about Pi's latest digits is a mathematician's joke.

However, for information, the last 100 digits of Pi calculated (2022 record) are: 4, 2, 9, 3, 0, 2, 4, 2, 3, 5, 1, 4, 1, 4, 4, 0, 6, 0, 6, 8, 5, 3, 2, 0, 6, 9, 4, 5, 0, 7, 8, 4, 8, 7, 7, 6, 1, 7, 1, 6, 2, 4, 4, 4, 7, 2, 8, 5, 0, 0, 1, 4, 3, 2, 3, 6, 0, 8, 7, 5, 9, 4, 6, 3, 9, 7, 8, 3, 1, 4, 2, 9, 9, 9, 1, 8, 6, 6, 5, 7, 8, 3, 6, 4, 6, 6, 4, 8, 4, 0, 8, 5, 5, 8, 3, 7, 3, 9, 2, 6 and therefore the last (known) digit of Pi is 6 (six).

The Feynman point is a sequence of six consecutive 9s (999999) that appears early in the decimal places of Pi, precisely at the 762nd decimal place. Richard Feynman, a renowned physicist, mentioned this phenomenon as a mathematical curiosity and pointed out that he would like to memorize and recite the decimals of π until he arrives at nine,nine,nine,nine,nine,nine to finish with and so on! in order to make a layman who would listen to him believe that π is a rational number.