4294967295

4294967295
Cardinal four billion two hundred ninety-four million nine hundred sixty-seven thousand two hundred ninety-five
Ordinal 4294967295th
(four billion two hundred ninety-four million nine hundred sixty-seven thousand two hundred and ninety-fifth)
Factorization 3 × 5 × 17 × 257 × 65537
Roman numeral N/A
Binary 111111111111111111111111111111112
Ternary 1020020222012211112103
Quaternary 33333333333333334
Quinary 322440024231405
Senary 15501040155036
Octal 377777777778
Duodecimal 9BA46159312
Hexadecimal FFFFFFFF16
Vigesimal 3723AI4F20
Base 36 1Z141Z336

The number 4,294,967,295 is an integer equal to 232 − 1. It is a perfect totient number.[1][2] It has a factorization of 3 \cdot 5 \cdot 17 \cdot 257 \cdot 65537. Since these factors are the five known Fermat primes, this number is the largest known odd value n for which a regular n-sided polygon is constructible using compass and straightedge.[3][4] Equivalently, it is the largest known odd number n for which the angle 2\pi/n can be constructed, or for which \cos(2\pi/n) can be expressed in terms of square roots.

In computing

The number 4,294,967,295, equivalent to the hexadecimal value FFFF,FFFF16, is the maximum value for a 32-bit unsigned integer in computing.[5] It is therefore the maximum value for a variable declared as an unsigned integer (unsigned, unsigned int, or unsigned long int) in many programming languages running on modern computers. The presence of the value may reflect an error, overflow condition, or missing value.

This value is also the largest memory address for CPUs using a 32-bit address bus.[6] Being an odd value, its appearance may reflect an erroneous (misaligned) memory address. Such a value may also be used as a sentinel value to initialize newly allocated memory for debugging purposes.

See also

References

  1. ↑ Loomis, Paul; Plytage, Michael; Polhill, John (2008). "Summing up the Euler φ Function". College Mathematics Journal 39 (1): 34–42.
  2. ↑ Iannucci, Douglas E.; Deng, Moujie; Cohen, Graeme L. (2003). "On perfect totient numbers" (PDF). Journal of Integer Sequences 6 (4): 03.4.5. MR 2051959.
  3. ↑ Lines, Malcolm E (1986). A Number for your Thoughts: Facts and Speculations About Numbers from Euclid to the latest Computers... (2 ed.). Taylor & Francis. p. 17. ISBN 9780852744956.
  4. ↑ "Sloane's A004729 : Divisors of 2^32 - 1 (for a(1) to a(31), the 31 regular polygons with an odd number of sides constructible with ruler and compass)", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ↑ Simpson, Alan (2005). "58: Editing the Windows Registry". Alan Simpson's Windows XP bible (2nd ed.). Indianapolis, Indiana: J. Wiley. p. 999. ISBN 9780764588969.
  6. ↑ Spector, Lincoln (19 November 2012). "Why can't 32-bit Windows access 4GB of RAM?". PC World. IDG Consumer & SMB. Archived from the original on 5 March 2016.
This article is issued from Wikipedia - version of the Thursday, March 17, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.