Find in Pi

Enter any sequence of digits — a birthday, a phone number, a lucky number, or any combination — to find where it first appears in the first 100 million decimal places of π. The search runs server-side against a pre-calculated file.

Why Does Every Number Eventually Appear in π?

The normality conjecture

A number is called normal in base 10 if every finite sequence of digits appears with exactly the frequency expected from pure chance. For a normal number, each digit 0–9 should occur about 10% of the time, each two-digit pair about 1%, and an 8-digit sequence like your birthday should appear roughly once in every 100 million digits. π is widely conjectured to be normal — meaning your phone number, birthday, or any digit sequence you can imagine would appear infinitely often in its infinite decimal expansion.

Why mathematicians believe it

The evidence is compelling. In the first trillion computed digits of π, each digit 0–9 appears almost exactly 10% of the time, and longer sequences follow the distribution expected of a random string. More fundamentally, almost all real numbers are normal in a rigorous mathematical sense — non-normal numbers are so rare they have probability zero. It would be extraordinarily surprising if π, with no obvious structural reason to be exceptional, turned out to be one of them.

What is proved — and what isn't

Despite overwhelming numerical evidence and centuries of effort, nobody has ever proved that π is normal. It has not even been proved that every digit 0–9 appears infinitely often — we believe it from data, not from a theorem. What is proved: π is irrational (its expansion never terminates or repeats) and transcendental (not the root of any polynomial with integer coefficients). Normality remains one of the great open problems of mathematics.

A π curiosity

The table below shows where each all-identical 6-digit sequence first appears in the first million decimal places of π.

Sequence	First decimal position
`000000`
`111111`
`222222`
`333333`
`444444`
`555555`
`666666`
`777777`
`888888`
`999999`

Frequently asked questions

What is π (pi)?

π (pi) is the ratio of a circle's circumference to its diameter. Its decimal expansion begins 3.14159265358979… and continues infinitely without repeating. It is an irrational and transcendental number.

How is the position counted?

Position 1 refers to the first digit after the decimal point of π, which is 1 (from 3.14159…). Position 2 is the second digit (4), and so on up to position 1,000,000.

What kinds of numbers can I search?

You can search any sequence of digits: birthdays (e.g. 19900314), phone numbers (digits only), zip codes, ID numbers, PIN codes, or any other integer sequence up to 20 digits long.

Why might my number not be found?

Longer sequences are naturally rarer. In the first 100 million decimal places of π, a specific 6-digit sequence is almost certain to appear. A 7-digit sequence has roughly a 99.995% chance of appearing at least once, an 8-digit sequence about 63%, and a 10-digit sequence about 1%. It is therefore normal for some long sequences not to appear in the first 100 million decimal places, even though they should appear somewhere in the infinite expansion of π if it is a normal number.

Does every number eventually appear in π?

Mathematicians conjecture that π is a "normal" number, meaning every finite sequence of digits appears infinitely often in its decimal expansion. However, this has not been proved. Statistically, most short sequences do appear within the first million digits.

The pre-calculated file is taken from pi2e.ch, the website on the 2016 22.4 trillion digits World record by Peter Trueb.