4,294,967,295

The number 4,294,967,295 is an integer equal to 232 − 1. It is a perfect totient number.[1][2] It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of .

4294967295
Cardinalfour billion two hundred ninety-four million nine hundred sixty-seven thousand two hundred ninety-five
Ordinal4294967295th
(four billion two hundred ninety-four million nine hundred sixty-seven thousand two hundred ninety-fifth)
Factorization3 × 5 × 17 × 257 × 65537
Greek numeral͵ζσϟε´
Roman numeralN/A
Binary111111111111111111111111111111112
Ternary1020020222012211112103
Octal377777777778
Duodecimal9BA46159312
HexadecimalFFFFFFFF16

In geometry

Since the prime factors of 232 − 1 are exactly 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 can be constructed, or for which can be expressed in terms of square roots.

Not only is 4,294,967,295 the largest known odd number of sides of a constructible polygon, but since constructibility is related to factorization, the list of odd numbers n for which an n-sided polygon is constructible begins with the list of factors of 4,294,967,295. If there are no more Fermat primes, then the two lists are identical. Namely (assuming 65537 is the largest Fermat prime), an odd-sided polygon is constructible if and only if it has 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 65537, 196611, 327685, 983055, 1114129, 3342387, 5570645, 16711935, 16843009, 50529027, 84215045, 252645135, 286331153, 858993459, 1431655765, or 4294967295 sides.[4] If there are more numbers in this list, they must be at least 2233+1 (approximately 102585827973), because every intervening Fermat number is known to be composite.[5]

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.[6] It is therefore the maximum value for a variable declared as an unsigned integer (usually indicated by the unsigned codeword) 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.[7] 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.

In 2004, 800 aircraft over Los Angeles were put in danger when the LA Air Route Traffic Control Center lost radio contact with all of the aircraft for about three hours, delaying 400 flights and cancelling 600, due to a computer design that kept time by starting at 4,294,967.295 seconds and counting down to zero, or 49 days, 17 hours, 2 minutes and 47.296 seconds. Some people were aware of this issue and the system needed to be restarted at least every 30 days. But the mistake was the choice of such a small number.[8]

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See also

References
  1. Loomis, Paul; Plytage, Michael; Polhill, John (2008). "Summing up the Euler φ Function". College Mathematics Journal. 39 (1): 34–42. JSTOR 27646564.
  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, N. J. A. (ed.). "Sequence 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. "Fermat Number". Wolfram MathWorld.
  6. Simpson, Alan (2005). "58: Editing the Windows Registry". Alan Simpson's Windows XP bible (2nd ed.). Indianapolis, Indiana: J. Wiley. p. 999. ISBN 9780764588969.
  7. 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.
  8. Matt Parker, Humble Pi, a Comedy of Math Errors, Chapter One, losing track of time, Penguin Random House UK
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