2,147,483,647

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 primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772.[2] Euler used trial division, improving on Pietro 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 the largest known prime until 1867.[4]

In computing, this number is the largest value that a signed 32-bit integer field can hold.

  1. ^ Weisstein, Eric W. "Double Mersenne Number". MathWorld. Wolfram Research. Retrieved 29 January 2018.
  2. ^ Dunham, William (1999). Euler: the master of us all. The Dolciani mathematical expositions. Washington, D.C.: Mathematical Association of America. p. 4. ISBN 978-0-88385-328-3.
  3. ^ Gautschi, Walter (1994). Gautschi, Walter (ed.). Mathematics of computation, 1943-1993: a half-century of computational mathematics ; Mathematics of Computation 50th Anniversary Symposium, August 9-13, 1993, Vancouver, British Columbia. Proceedings of symposia in applied mathematics. Vol. 48. Providence, RI: American Mathematical Society. p. 486. ISBN 978-0-8218-0291-5.
  4. ^ 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.