Back 2147483647 Catalan 2147483647 Czech 2147483647 German 2.147.483.647 Greek 2147483647 Spanish 2 147 483 647 (nombre) French 2,147,483,647 HE 2147483647 Hungarian 2147483647 Italian 2147483647 Korean
| 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 | MMCXLVMMCDLXXXMMMDCXLVII, or MMCXLVIICDLXXXMMMDCXLVII[1] |
| Binary | 11111111111111111111111111111112 |
| Ternary | 121121222121102021013 |
| Senary | 5530320055316 |
| Octal | 177777777778 |
| Duodecimal | 4BB2308A712 |
| Hexadecimal | 7FFFFFFF16 |
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.[2]
The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772.[3] Euler used trial division, improving on Pietro Cataldi's method, so that at most 372 divisions were needed.[4] 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.[5]
In computing, this number is the largest value that a signed 32-bit integer field can hold.
- ^ ACTUAL EVIDENCE OF ROMAN NUMERAL 2,147,483,647.
- ^ Weisstein, Eric W. "Double Mersenne Number". MathWorld. Wolfram Research. Retrieved 29 January 2018.
- ^ Dunham, William (1999). Euler: The Master of Us All. Washington, DC: Mathematical Association of America. p. 4. ISBN 978-0-88385-328-3.
- ^ Gautschi, Walter (1994). Mathematics of Computation, 1943–1993: A Half-Century of Computational Mathematics. Proceedings of Symposia in Applied Mathematics. Vol. 48. Providence, Rhode Island: American Mathematical Society. p. 486. ISBN 978-0-8218-0291-5.
- ^ 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.