2,147,483,647

Source: Wikipedia, the free encyclopedia.

2147483647
Cardinaltwo billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven
Ordinal2147483647th
(two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seventh)
Factorizationprime
Prime105,097,565th
Greek numeral͵γχμζ´
Roman numeralN/A
Binary11111111111111111111111111111112
Ternary121121222121102021013
Senary5530320055316
Octal177777777778
Duodecimal4BB2308A712
Hexadecimal7FFFFFFF16
By 1772, Leonhard Euler had proven that 2,147,483,647 is a prime.

The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes.[1]

The

largest known prime until 1867.[4]

In computing, this number is the largest value that a

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, not anticipating future interest in perfect numbers, 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.[5]

He repeated this prediction in his work from 1814, A New Mathematical and Philosophical Dictionary.[6][7]

In fact, a larger prime was discovered in 1855 by Thomas Clausen (67,280,421,310,721), though a proof was not provided. Furthermore, 3,203,431,780,337 was proven to be prime in 1867.[4]

In computing

The number 2,147,483,647 (or

overflow condition, or missing value.[citation needed
]

The data type

UTC 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-bit time_t type are susceptible to the Year 2038 problem.[9]

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.[10]

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

unsigned instead of signed 32-bit integer is used, the limit might be extended to 4,294,967,295.[11]

References

  1. ^ Weisstein, Eric W. "Double Mersenne Number". MathWorld. Wolfram Research. Retrieved 29 January 2018.
  2. ISBN 978-0-88385-328-3
    .
  3. ISBN 978-0-8218-0291-5
    .
  4. ^ a b Caldwell, Chris (8 December 2009). "The Largest Known Prime by Year: A Brief History". The Prime Pages. University of Tennessee at Martin. Retrieved 29 January 2018.
  5. ^ Barlow, Peter (1811). An Elementary Investigation of the Theory of Numbers. London: J. Johnson & Co. p. 43. greatest.
  6. ^ Barlow, Peter (1814). 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. London: G. and S. Robinson.
  7. ISBN 978-0-8218-2824-3
    .
  8. IEEE and The Open Group. The Open Group. 2004. Archived from the original
    on 19 December 2008. Retrieved 7 March 2008.
  9. ^ "The Year-2038 Bug". Archived from the original on 18 March 2009. Retrieved 9 April 2009.
  10. ^ Abrams, Lawrence. "Microsoft Exchange year 2022 bug in FIP-FS breaks email delivery". Bleeping Computer. Retrieved 2 January 2022.
  11. ^
    ISBN 978-1-136-14525-4
    .
  12. ^ By (19 September 2018). "Final Fantasy Exploit Teaches 32-bit Integer Math". Hackaday. Retrieved 25 September 2022.
  13. ^ "32-Bit Integers and Why Old Computers Matter". www.vice.com. 12 April 2015. Retrieved 25 September 2022.
  14. ^ "Coins". Runescape Official Wiki.
  15. ^ Wood, Austin (12 July 2018). "Old School Runescape pulled offline as billions of gold appear out of nowhere". PC Gamer. Retrieved 25 September 2022. 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.

External links

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