2147483647

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)
Greek numeral͵γχμζ´
Roman numeralMMCXLVMMCDLXXXMMMDCXLVII, or MMCXLVIICDLXXXMMMDCXLVII
Binary11111111111111111111111111111112
Ternary121121222121102021013
Quaternary13333333333333334
Quinary133442234340425
Senary5530320055316
Octal177777777778
Duodecimal4BB2308A712
Hexadecimal7FFFFFFF16
Vigesimal1DB1F92720
Base 36ZIK0ZJ36

2,147,483,647 or 2147483647 is a Mersenne prime. It is the result of 231−1, and it is one of only four known double Mersenne primes. 2,147,483,647 was the largest known prime number until 1867. It is also the largest possible unsigned 32 bit integer.

Barlow's prediction

In the year 1772, Leonhard Euler showed that 2,147,483,647 is a prime.

At the time of its discovery, 2,147,483,647 was the largest known prime number. In 1811, Peter Barlow wrote:

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.

He repeated this prediction in his work from 1814, A New Mathematical and Philosophical Dictionary. Then, in 1867, the number 3,203,431,780,337 was proven to be prime.

Notes

  1. ↑ Peter Barlow wrote it in An Elementary Investigation of the Theory of Numbers

References

  1. ↑ Wolfram Alpha.
  2. ↑ MyTecBits.
  3. ↑ Weisstein, Eric W. "Double Mersenne Number". MathWorld. Wolfram Research. Retrieved January 29, 2018.
  4. 1 2 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. OCLC 1191003275.
  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. OCLC 889473251.
  7. ↑ Shanks, Daniel (2001). Solved and Unsolved Problems in Number Theory (4th ed.). Providence, Rhode Island: American Mathematical Society. p. 495. ISBN 978-0-8218-2824-3.