| 2147483647 | |
|---|---|
| Cardinal | two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven |
| Ordinal | 2147483647th (two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seventh) |
| Factorization | prime |
| Prime | 105,097,565th |
| Greek numeral | ͵γχμζ´ |
| Roman numeral | N/A,n/a |
| Binary | 11111111111111111111111111111112 |
| Ternary | 121121222121102021013 |
| Senary | 5530320055316 |
| Octal | 177777777778 |
| Duodecimal | 4BB2308A712 |
| Hexadecimal | 7FFFFFFF16 |
Thenumber2147483647 is the eighthMersenne prime, equal to 231 − 1. It is one of only four knowndouble Mersenne primes.[1]
Theprimality of this number was proven byLeonhard Euler, who reported the proof in a letter toDaniel Bernoulli written in 1772.[2] Euler usedtrial division, improving onPietro Cataldi's method, so that at most 372 divisions were needed.[3] It thus improved upon the previous record-holding prime, 6,700,417 – also discovered by Euler – forty years earlier. The number 2,147,483,647 remained thelargest known prime until 1867.[4]
In computing, this number is the largest value that asigned32-bit integer field can hold.
At the time of its discovery, 2,147,483,647 was thelargest known prime number. In 1811,Peter Barlow wrote (inAn Elementary Investigation of the Theory of Numbers):
Euler ascertained that 231 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the aboveperfect numbers [i.e., 230(231 − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they are merely curious, without being useful, it is not likely that any person will attempt to find one beyond it.[5]
He repeated this prediction in his work from 1814,A New Mathematical and Philosophical Dictionary.[6][7]
A larger prime, 67,280,421,310,721, was discovered in 1855 byThomas Clausen, but he did not provide a proof. In 1867, the number 3,203,431,780,337 was proven to be prime.[4]
The number 2,147,483,647 (orhexadecimal 7FFFFFFF16) is the maximum positive value for a32-bitsigned binary integer incomputing. It is therefore the maximum value for variables declared as integers (e.g., asint) in many programming languages.
The data typetime_t, used on operating systems such asUnix, is a signed integer counting the number of seconds since the start of theUnix epoch (midnightUTC of 1 January 1970), and is often implemented as a 32-bit integer.[8] The latest time that can be represented in this form is 03:14:07 UTC on Tuesday, 19 January 2038 (corresponding to 2,147,483,647 seconds since the start of the epoch). This means that systems using a 32-bittime_t type are susceptible to theYear 2038 problem.[9]
On 1 January 2022, a bug was reported forMicrosoft Exchange systems where email delivery would fail. An internal malware scanner (enabled by default since 2013) used the date and time as a signed 32-bit integer. The integer would change during the new year to 2,201,010,001 (with the first two digits representing the year), surpassing the maximum value for this data type.[10]
The number 2,147,483,647 often becomes a hard limit for various statistics in video games, such as points or money, if they are represented by signed 32-bit integers (rather thanfloating-point,double-precision orarbitrary-precision).[11][12] Going over this limit by legitimate means, or by modding or hacking the game, results in many different outcomes caused byinteger overflow.[13] The most common outcome is the number "wrapping" into the negatives. Another potential outcome isgame crashing, thus meaning there was no failsafe implemented in the event the value exceeds the signed 32-bit limit—generally if the underlying engine has undefined behavior, instead of a wraparound behavior, for integer overflow. A well-known example in video games is that ofOld School RuneScape andGrand Theft Auto V, where the number is used as the maximum amount of coins (or any other item) that a player can hold at once with normal methods, known as a "max cash stack".[14][15] In similar cases, where anunsigned instead of signed 32-bit integer is used, the limit might be extended to4,294,967,295.[11]
it's appropriate to check that the calculation doesn't overflow the max integer limit of the game's language (2.1 billion). Unfortunately, the logic used for this calculation was incorrect, and when executed on stacks of other items (not the pouch itself) the result was to convert the stack to 2.1b coins.