Very large numbers
There is no biggest number: add one to any number and you have a larger one. What there is instead is a set of thresholds — where words run out, where ordinary computer arithmetic stops being exact, and where a figure stops being a count and becomes an estimate. This page is about those thresholds, because almost every confusing thing about large numbers happens at one of them.
Three kinds of large number, written the same way
"100,000,000,000" could be an exact count, a rough estimate, or a way of saying "about this big". The digits look identical and the three mean quite different things, so the first question about any large number is which of these it is.
An exact integer
Every digit is meant. A number like this comes from counting or from a definition, so it does not drift, and writing one digit wrong makes it a different number rather than a slightly worse estimate.
A measured quantity
The figure is the middle of a range. Trailing zeros mark where the measurement ran out rather than digits that happen to be zero, so quoting more of them than the source supports invents precision that was never there.
A magnitude
Only the size is being claimed. A magnitude is usually written as a power of ten because the digits would carry no information a reader could use, and two magnitudes an order apart are different answers even when both are 'about a lot'.
The practical test is what happens if you change the last digit. Change the last digit of the IPv4 address count and it is simply wrong. Change the last digit of an estimate of the number of stars in the galaxy and nothing has happened at all, because that digit was never a claim.
What a billion means
Not one thing. The short scale, used throughout English today, moves up by a factor of a thousand at each name. The long scale, still current across much of continental Europe and Latin America, moves up by a factor of a million, and puts separate words — milliard, billiard — at the steps in between. Britain switched from the long scale to the short in the 1970s.
This site uses the short scale everywhere, which is worth saying out loud rather than assuming: the two conventions disagree by a factor of a thousand at the first word most people use for a big number.
One thousand — 103
About the number of people a person can recognise by face.
One million — 106
A million seconds is eleven and a half days. Both scales agree here.
One billion — 109
A billion seconds is about thirty-two years. This is the first word the two scales disagree about, and the disagreement is a factor of a thousand.
On the short scale a billion is 10⁹; on the long scale it is 10¹², larger by a factor of 10³. On the long scale, 10⁹ is called a milliard.
One trillion — 1012
A trillion seconds is about thirty-one thousand seven hundred years — back past the last ice age.
On the short scale a trillion is 10¹²; on the long scale it is 10¹⁸, larger by a factor of 10⁶. On the long scale, 10¹² is called a billion.
One quadrillion — 1015
Roughly the number of ants alive at any moment, which is about the largest count of real things this word gets used for.
On the short scale a quadrillion is 10¹⁵; on the long scale it is 10²⁴, larger by a factor of 10⁹. On the long scale, 10¹⁵ is called a billiard.
One quintillion — 1018
About the number of grains of sand on Earth's beaches, on the usual estimate. Past here, powers of ten are clearer than words.
On the short scale a quintillion is 10¹⁸; on the long scale it is 10³⁰, larger by a factor of 10¹². On the long scale, 10¹⁸ is called a trillion.
The numbers people mean by "the biggest number"
There is no biggest number, and saying only that answers a question nobody asked. What the question usually means is one of these — the largest number with a name, the largest anyone has had a reason to write down, or the largest that has actually been proved something about. They have different answers, and every one of them is more interesting than the refusal.
A googol — 10¹⁰⁰ — a 1 followed by a hundred zeros
Larger than the estimated number of atoms in the observable universe by about twenty orders of magnitude, so it counts nothing physical.
Named in the 1930s by the nine-year-old nephew of the mathematician Edward Kasner, who wanted a word for a number that was large but finite. The search engine is a misspelling of it.
A googolplex — 10 to the power of a googol
It cannot be written out. There is not enough matter in the observable universe to record its digits, even one digit per atom.
Coined alongside the googol as the answer to 'what comes after that', and it is the first number most people meet that is unwritable rather than merely long.
Graham's number — So large that ordinary exponent notation cannot express it
Its size needs a notation built for the purpose. Even the number of arrows in that notation is itself defined by a tower of the same construction repeated sixty-four times.
An upper bound in a 1971 combinatorics proof about colouring the corners of a high-dimensional cube. It was the largest number ever used in a serious mathematical proof for decades. The last digits are known even though the number is not — the final digit is 7.
The largest known prime — Over 41 million digits
A Mersenne prime, of the form 2ⁿ − 1. Printed at ordinary book density it would fill several thousand pages, and it is the largest number anyone has actually proved anything about.
Found by distributed computing in 2024. Mersenne numbers dominate the record because a special test exists for exactly that form — the record is a fact about which numbers are cheap to test, not about which are large.
Four thresholds, worked
Everything stated below is computed exactly, at whatever size the number happens to be. Digit counts, parity, digit sums and powers of two stay cheap and stay exact however many digits there are — it is factorising and primality that get expensive, not arithmetic in general.
A million — 7 digits
The last scale word most people have a physical sense of.
1000000
- 7 digits long.
- Even.
- Exactly 10 to the power of 6.
- Its digits sum to 1, giving a digital root of 1.
- Divisible by 2, 5.
2⁵³ — 16 digits
The point where ordinary computer arithmetic stops being exact. Above this, a JavaScript number cannot represent every integer, so 2⁵³ and 2⁵³ + 1 become the same value — which is why this site stores every number as text rather than as a number.
9007199254740992
- 16 digits long.
- Even.
- Exactly 2 to the power of 53.
- Its digits sum to 77, giving a digital root of 5.
- Divisible by 2.
Past the point where this site computes factors, divisors or primality. What is listed above is everything it can establish without guessing.
2⁶³ − 1 — 19 digits
The largest signed 64-bit integer, and what a great deal of software means by 'huge'.
9223372036854775807
- 19 digits long.
- Odd.
- Its digits sum to 88, giving a digital root of 7.
- Divisible by 7.
Past the point where this site computes factors, divisors or primality. What is listed above is everything it can establish without guessing.
2¹²⁸ — 39 digits
The size of the IPv6 address space. Thirty-nine digits, and still an exact integer with every digit meant.
340282366920938463463374607431768211456
- 39 digits long.
- Even.
- Exactly 2 to the power of 128.
- Its digits sum to 166, giving a digital root of 4.
- Divisible by 2.
Past the point where this site computes factors, divisors or primality. What is listed above is everything it can establish without guessing.
A ladder of real quantities
Scale words are hard to feel because they all sound similar. Real things at each size are easier. Every rung below is one quantity from this catalogue, one power of ten apart, and each step up multiplies the one below it by ten.
| Size | Something that big | Kind of claim |
|---|---|---|
| 103 | 6 thousand exoplanets confirmed | Measured |
| 104 | 20 thousand breaths taken in a day | Approximate |
| 105 | 100 thousand commercial flights each day | Approximate |
| 106 | 1 million asteroids with catalogued orbits | Approximate |
| 107 | 21 million bitcoin that will ever exist | Exact |
| 108 | 500 million alveoli in a pair of adult human lungs | Approximate |
| 109 | 4 billion addresses available in IPv4 | Approximate |
| 1010 | 25 billion chickens alive at any moment | Approximate |
| 1011 | 150 billion base pairs in the genome of the plant Paris japonica | Approximate |
| 1012 | 2 trillion galaxies in the observable universe | Estimated |
| 1013 | 38 trillion bacteria living in and on an adult human body | Estimated |
| 1014 | 281 trillion possible MAC addresses | Defined |
| 1016 | 20 quadrillion ants alive at any moment | Estimated |
| 1018 | 5 × 10¹⁸ kilograms the mass of the Earth's atmosphere | Approximate |
| 1019 | 1 × 10¹⁹ atoms in a grain of sand | Estimated |
| 1021 | 1 × 10²¹ bytes in a zettabyte | Exact |
| 1024 | 6 × 10²⁴ kilograms the mass of the Earth | Approximate |
| 1026 | 4 × 10²⁶ watts the power output of the Sun | Approximate |
| 1027 | 2 × 10²⁷ kilograms the mass of Jupiter | Approximate |
| 1030 | 1 × 10³⁰ bacteria on Earth | Estimated |
| 1036 | 5 × 10³⁶ possible values of a version-4 UUID | Approximate |
| 1038 | 340 × 10³⁶ addresses in the IPv6 address space | Defined |
| 1077 | 1 × 10⁷⁷ possible outputs of the SHA-256 hash function | Defined |
| 1080 | 1 × 10⁸⁰ atoms of ordinary matter | Estimated |
The last column is doing real work. Two quantities can sit on the same rung and be entirely different kinds of statement — one counted, one estimated from a sample — and reading them as equally certain is the commonest mistake made with big numbers.
Exact — A count or a definition. Every digit is meant, and changing one makes it a different number rather than a slightly worse answer.
Defined — Fixed by agreement rather than found by measuring. The figure has no error bar because measuring it more precisely refines the unit instead.
Measured — The result of measuring something, quoted to the precision the measurement supports.
Estimated — A central figure with a real spread around it, stated alongside. The spread is part of the claim, not an aside.
Approximate — Rounded so a reader can hold it. The underlying source is more precise, and the trailing zeros are not digits.
Eight numbers with no profile of their own
These were considered for their own pages and turned down, because a number profile here leads with a mathematical analysis and none of these can have one at a sensible cost. A page whose main section is missing is a worse answer than no page. But "we will not give this its own page" is not the same claim as "there is nothing to say about this", and six of the eight have real structure that is the whole point of them.
2¹²⁸ — an exact integer
The number of addresses in the IPv6 address space.
An IPv6 address is 128 bits, so the space is 2¹²⁸. It is written as a power because the 39 digits carry nothing a reader can hold — the exponent is the fact.
340282366920938463463374607431768211456
2⁶⁴ — an exact integer
The number of distinct values a 64-bit word can hold.
The reason a 64-bit computer can address more memory than anyone will build. The previous generation's 2³² ran out in ordinary use; this one has not come close.
18446744073709551616
2⁶³ − 1 — an exact integer
The largest signed 64-bit integer.
One bit of the 64 carries the sign, so the positive range stops one short of 2⁶³. This is the number a great deal of software silently means by 'the biggest number'.
9223372036854775807
2⁶⁴ − 1 — an exact integer
The largest unsigned 64-bit integer.
The same 64 bits with no sign bit to pay for. Adding one to it wraps round to zero on most hardware, which is a whole family of bugs.
18446744073709551615
2⁶¹ − 1 — an exact integer
A Mersenne prime, and the ninth to be found.
Proved prime by Pervushin in 1883, by hand. It is still the largest prime that fits comfortably in a machine word, which is why it turns up in hash functions.
2305843009213693951
43,252,003,274,489,856,000 — an exact integer
The number of reachable positions on a 3×3×3 Rubik's Cube.
8! × 3⁷ × 12! × 2¹¹, halved — the corner and edge arrangements, divided by the rearrangements the mechanism cannot reach. Every one of them is at most twenty moves from solved.
43252003274489856000
A light-year in metres — a measured quantity
The distance light travels in a Julian year, in metres.
Filed beside 2¹²⁸ when it was withdrawn, which was the mistake: one is a combinatorial fact and the other is a unit conversion. They fail the same ceiling for entirely different reasons.
Exact by construction rather than by measurement: the metre, the second and the Julian year are all defined, so this conversion has no error bar. What it is not is a counted quantity — it is a unit written in different units.
9460730472580800
A parsec in metres — a measured quantity
The distance at which one astronomical unit subtends one arcsecond.
Exact since 2015, when the IAU fixed the parsec as exactly 648000/π astronomical units. Before that it was a definition that depended on a measurement.
30856775814913673
The last two are a different case from the first six, and grouping them together was a mistake worth naming. A light-year in metres is not a large integer that happens to be hard to factorise; it is a measurement written in small units. Its size says something about the metre, not about the number.
Where this site stops
Two separate limits, often confused, and both worth stating plainly.
Exactness has no limit here
Every number on this site is stored as text, not as a machine number, so no value is ever rounded on its way into or out of the catalogue. Above 2⁵³ an ordinary computer number silently loses the ability to tell consecutive integers apart; storing digits as digits avoids that entirely.
Analysis does have a limit
Factorising a number, or proving it prime, costs far more than reading it. Past roughly a million million, this site stops computing those properties rather than make a page slow or an answer approximate. What it can still say — digit count, parity, digit sum, exact powers, small divisors — it says, and it does not pad the gap with anything softer.
You can see the difference on any large profile: the number itself is exact to the last digit, and the mathematics section is either complete or absent. There is no middle state where a property is guessed, because a guessed property about a rounded number is a confident statement about a different number. More on how this is decided in the methodology.
Common questions
What is the biggest number?
There isn't one. Whatever number you name, adding one to it gives a larger number, so the counting numbers have no largest member. Questions that sound like this usually mean something narrower and answerable: the largest number with a name, the largest prime anyone has found, or the largest value a particular computer can hold — and those have different answers.
Does a billion mean the same thing everywhere?
No. On the short scale, used in English today, a billion is 10⁹ — a thousand million. On the long scale, still used across much of continental Europe and Latin America, a billion is 10¹² — a million million, a thousand times larger. Britain used the long scale until the 1970s. This site uses the short scale throughout.
What is a googol?
A googol is 10¹⁰⁰ — a 1 followed by a hundred zeros. It was named by a mathematician's nine-year-old nephew in the 1930s. It is larger than the estimated number of atoms in the observable universe by about twenty orders of magnitude, which means it counts nothing physical; it exists to make the point that numbers keep going after the things they might count run out.
Why do some number pages here have no mathematics section?
Because the number is too large to analyse honestly. Testing whether a number is prime, or listing its factors, gets expensive very quickly, and doing it on a value that has been rounded would produce confident answers about a different number. Above the limit, this site says what it can establish exactly — how many digits, whether it is even, whether it is a power of two — and does not guess at the rest.
What is the largest number a computer can hold?
It depends entirely on how many bits are set aside for it. A signed 64-bit integer, the most common choice, stops at 9,223,372,036,854,775,807 — that is 2⁶³ − 1, one short of 2⁶³ because one of the 64 bits carries the sign. An unsigned 64-bit integer reaches 2⁶⁴ − 1. Adding one more to either usually wraps round rather than raising an error, which is a well-known source of bugs.