2,147,483,647

April 2022 January 2018 2147483647 two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven prime 105,097,565th thumb|upright|By 1772, Leonhard Euler had proven that 2,147,483,647 is a prime. The number 2147483647Pronounced two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven.Vanovschi Vitalii Properties of the number 2147483647 http://www.numberempire.com:80/2147483647 2026-09-01 www.numberempire.com en is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes.Weisstein Eric W. https://mathworld.wolfram.com/DoubleMersenneNumber.html Double Mersenne Number MathWorld Wolfram Research 29 January 2018 The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772.Dunham William https://archive.org/details/eulermasterofusa0000dunh Euler: the master of us all Mathematical Association of America 1999 978-0-88385-328-3 The Dolciani mathematical expositions Washington, D.C. 4 registration Euler used trial division, improving on Pietro Cataldi's method, so that at most 372 divisions were needed.Gautschi Walter Mathematics of computation, 1943-1993: a half-century of computational mathematics; Mathematics of Computation 50th Anniversary Symposium, August 9-13, 1993, Vancouver, British Columbia American Mathematical Society 1994 978-0-8218-0291-5 Gautschi Walter Proceedings of symposia in applied mathematics 48 Providence, RI 486 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 the largest known prime until 1867.Caldwell Chris 8 December 2009 https://primes.utm.edu/notes/by_year.html The Largest Known Prime by Year: A Brief History The Prime Pages University of Tennessee at Martin 29 January 2018 In computing, this number is the largest value that a signed 32-bit integer field can hold. Barlow's prediction At the time of its discovery, 2,147,483,647 was the largest known prime number. In 1811, Peter Barlow wrote (in An 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 above perfect 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.Barlow Peter Peter Barlow (mathematician) https://archive.org/details/anelementaryinv00barlgoog An Elementary Investigation of the Theory of Numbers J. Johnson & Co. 1811 London 43 1191003275 He repeated this prediction in his work from 1814, A New Mathematical and Philosophical Dictionary.Barlow Peter Peter Barlow (mathematician) https://books.google.com/books?id=Y-csAAAAYAAJ&q=2147483647&pg=PT544 A New Mathematical and Philosophical Dictionary: Comprising an Explanation of Terms and Principles of Pure and Mixed Mathematics, and Such Branches of Natural Philosophy as Are Susceptible of Mathematical Investigation G. and S. Robinson 1814 London 889473251Shanks Daniel Solved and Unsolved Problems in Number Theory American Mathematical Society 2001 978-0-8218-2824-3 4th Providence, Rhode Island 495 In 1867, the number 3,203,431,780,337 was proven to be prime. In computing The number 2,147,483,647 (or hexadecimal 7FFFFFFF16) is the maximum positive value for a 32-bit signed binary integer in computing. It is therefore the maximum value for variables declared as integers (e.g., as int) in many programming languages. The data type time_t, used on operating systems such as Unix, is a signed integer counting the number of seconds since the start of the Unix epoch (midnight UTC of 1 January 1970), and is often implemented as a 32-bit integer.2004 The Open Group Base Specifications Issue 6 IEEE Std 1003.1, 2004 Edition (definition of epoch) http://www.opengroup.org/onlinepubs/000095399/ live https://web.archive.org/web/20081219153936/http://www.opengroup.org/onlinepubs/000095399/ 19 December 2008 7 March 2008 IEEE and The Open Group The Open Group 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-bit time_t type are susceptible to the Year 2038 problem.http://www.2038bug.com/ The Year-2038 Bug 9 April 2009 https://web.archive.org/web/20090318084855/http://www.2038bug.com/ 18 March 2009 live On 1 January 2022, a bug was reported for Microsoft 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.Abrams Lawrence January 1, 2022 Microsoft Exchange year 2022 bug in FIP-FS breaks email delivery https://www.bleepingcomputer.com/news/microsoft/microsoft-exchange-year-2022-bug-in-fip-fs-breaks-email-delivery/ 2 January 2022 Bleeping Computer In video games 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 than floating-point, double-precision or arbitrary-precision).Lever Nik https://books.google.com/books?id=eV0My6PR9xIC&pg=PA149 Director MX 2004 Games: Game Development with Director 2012-08-06 Taylor & Francis 978-1-136-14525-4 enCockfield Bryan 2018-09-19 Final Fantasy Exploit Teaches 32-bit Integer Math https://hackaday.com/2018/09/19/final-fantasy-exploit-teaches-32-bit-integer-math/ 2022-09-25 Hackaday Going over this limit by legitimate means, or by modding or hacking the game, results in many different outcomes caused by integer overflow.Byrne Michael 12 April 2015 32-Bit Integers and Why Old Computers Matter https://www.vice.com/en/article/32-bit-integers-and-why-old-computers-matter/ 2022-09-25 Vice The most common outcome is the number "wrapping" into the negatives. Another potential outcome is game 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 of Old School RuneScape and Grand 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". Coins https://runescape.wiki/w/Coins Runescape Official WikiWood Austin 2018-07-12 Old School Runescape pulled offline as billions of gold appear out of nowhere en PC Gamer https://www.pcgamer.com/old-school-runescape-pulled-offline-as-billions-of-gold-appear-out-of-nowhere/ 2022-09-25 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. In similar cases, where an unsigned instead of signed 32-bit integer is used, the limit might be extended to 4,294,967,295. Notes References External links Prime curios: 2147483647 10 Category:Integers Category:Prime numbers