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Topic: 4294967297 (number)

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English language numerals

	600 (number)
		Six hundred is the natural number following five hundred ninety-nine and preceding six hundred one.
		641 prime number, factor of 4294967297 (the smallest nonprime Fermat number)
		This number is the magic constant of nxn magic square and n-Queens Problem for n = 11.
	pedia.newsfilter.co.uk /wikipedia/6/60/600__number_.html (892 words)

	fermat number (Site not responding. Last check: 2007-10-13)
		The following heuristic argument suggests there are only finitely many Fermat primes: according to the prime number theorem, the "probability" that a number n is prime is at most A/ln(n), where A is a fixed constant.
		For one thing, the argument assumes that Fermat numbers behave "randomly", yet we have already seen that the factors of Fermat numbers have special properties.
		There are a number of conditions that are equivalent to the primality of F
	www.yourencyclopedia.net /fermat_number.html (961 words)

	Ivars Peterson's MathTrek - Cracking Fermat Numbers
		In 1640, French mathematician Pierre de Fermat (1601–1665) conjectured that all such numbers are primes, based on the observation that the first five are prime numbers.
		As of Feb. 25, 212 Fermat numbers were known to be composite, and searchers had found a total of 245 prime factors.
		The divisor itself is the fifth largest known prime number, and it is the largest that is not a Mersenne prime.
	www.maa.org /mathland/mathtrek_03_03_03.html (591 words)

	Fermat prime. Who is Fermat prime? What is Fermat prime? Where is Fermat prime? Definition of Fermat prime. Meaning of ...
		A Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form
		Fermat numbers and Fermat primes were first studied by Pierre de Fermat, who conjectured that all Fermat numbers are prime.
		Since at least the time of Euclid, it was known that many regular polygons were capable of being constructed by ruler and compass.
	www.knowledgerush.com /kr/encyclopedia/Fermat_prime (958 words)

	Prime numbers
		The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties.
		A pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa.
		The statement that the density of primes is 1/log(n) is known as the Prime Number Theorem.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Prime_numbers.html (1589 words)

	Fermat Numbers (Site not responding. Last check: 2007-10-13)
		Fermat was greatly interested in numbers and number theory.
		He devised a set of numbers which are now called ‘Fermat numbers’.
		Fermat created this set as he believed that this set of numbers were all prime and still did until the day that he died.
	students.bath.ac.uk /ma3pab/numbers.html (81 words)

	600 (number) - Iridis Encyclopedia (Site not responding. Last check: 2007-10-13)
		It is a pronic number and a Harshad number.
		641 prime number, Sophie Germain prime, factor of 4294967297 (the smallest nonprime Fermat number)
		683 prime number, Sophie Germain prime, sum of five consecutive primes (127 + 131 + 137 + 139 + 149)
	www.iridis.com /613_(number) (919 words)

	Sequence A000215, Fermat Numbers at MROB
		The Fermat numbers, Sloane's A000215, are numbers of the form 2
		In the years since the Fermat numbers and their factors have been the subject of much research.
		This limits the number of primes that must be tested to factor a given Fermat number.
	home.earthlink.net /~mrob/pub/math/seq-a000215.html (197 words)

	Primes and square roots
		The explanation went like this: "When a number is divided by another number that is greater than its square root, the result is a number smaller than the square root.
		Suppose n is a number and a, (a not equal to n) is a factor of n with a greater then the square root of n.
		So, you need to try to divide 4294967297 by 257; it takes a long time and you get a remainder of 1, so 257 is not a factor of 4294967297.
	mathcentral.uregina.ca /QQ/database/QQ.09.00/paul2.html (1000 words)

	Numbers
		Abundant numbers are numbers whose factors add up to more than the number.
		Complex numbers are in the form a+bi, where i is the square root of negative one.
		There are very few perfect numbers, this is because all perfect numbers are the sum of all the numbers from one to a mersenne prime.
	campus.fortunecity.com /newton/970/numbers.html (859 words)

	Science Fair Projects - 600 (number)
		607 prime number, sum of three consecutive primes (197 + 199 + 211), Mertens function(607) = 0, area code of Ithaca, New York
		610 = 2 × 5 × 61, sphenic number, nontotient.
		659 prime number, Sophie Germain prime, sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Mertens function sets new low of -10 which stands until 661, highly cototient number
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/600_(number) (1133 words)

	Number Theory - Primes
		A number n > 1 that is not prime is said to be composite.
		We take the minimum of each exponent because we need a number that divides both m and n, but is as large as possible.
		Fermat conjectured that all of the Fermat numbers are prime, but Euler found the factor 641 of F
	www.csm.astate.edu /~rossa/cs6623/number2.html (375 words)

	Fermat Number (Site not responding. Last check: 2007-10-13)
		Prime and Eisenstein (1844) proposed as a problem the proof that there are an infinite number of Fermat primes (Ribenboim 1996, p.
		Factoring Fermat numbers is extremely difficult as a result of their large size.
		Tables of known factors of Fermat numbers are given by Keller (1983), Brillhart et al.
	mathserver.sdu.edu.cn /mathency/math/f/f079.htm (577 words)

	Math Trek: Cracking Fermat Numbers, Science News Online, March 1, 2003 (Site not responding. Last check: 2007-10-13)
		What's striking about the sequence is the rapidity with which the size of the numbers grows larger.
		With the advent of computers and, recently, a concerted effort to use the spare processing power of computers around the world to test for divisors of Fermat numbers (see http://www.fermatsearch.org/), the search for factors has expanded considerably.
		John B. Cosgrove describes the discovery of the largest known composite Fermat number at http://www.spd.dcu.ie/johnbcos/.
	www.sciencenews.org /articles/20030301/mathtrek.asp (699 words)

	The CTK Exchange Forums (Site not responding. Last check: 2007-10-13)
		It's easy enough to tell whether a binary number is divisible by 4, 8, and, in general, by any other power of 2.
		I meant to ask not whether tests existed for divisibility of even numbers expressed in binary by some particular number (4, 8, 11, etc.) but whether one can tell by inspection whether any even binary number (which may not be divisible 4, 8, 11, 3, etc.) nonetheless has some divisor other than 2.
		Fermat conjectured the number 2^32 1 was prime (circa 1640).
	www.cut-the-knot.com /htdocs/dcforum/DCForumID6/290.shtml (531 words)

	Euler's Contribution To Number Theory (Site not responding. Last check: 2007-10-13)
		Euler found that the fifth Fermat number, 4294967297, is divisible by 641.
		After the fifth Fermat number was disproven to be prime, it is unlikely that the any higher Fermat number was ever shown to have a divisor greater than one during the time of Euler.
		Just because the fifth Fermat number was disproven to be prime, does not necessarily mean that higher numbers were not prime.
	sweb.uky.edu /~jrbail01/euler.htm (1273 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Because each prime is multiplied only once in our product of prime numbers, each prime pi can only divide either n or m.
		This, however, contradicts the theorem that every integer is divisible by some prime number.
		In the end, the unmarked numbers are prime.
	home.olemiss.edu /~aldunn/pres.ppt (406 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Most Useful Program: Albert van der Horst Albert van der Horst S P&A R&C Oranjestraat 8 3511 RA UTRECHT The Netherlands Judges' comments: For a canned example: make albert albert 1234567890123456789 We were impressed with the speed at which it was able to factor arbitrarily large numbers consisting of factors that fit into a long.
		It quits as soon as there is at most one factor left, but that factor will not be shown.
		To customize the program into a factorizer of a fixed number, use cc albert.c -o 4294967297 or some such.
	www.acc.umu.se /~balp/ioccc/1992/albert.hint (510 words)

	600 (number) - Enpsychlopedia (Site not responding. Last check: 2007-10-13)
		607 prime number, sum of three consecutive primes (197 + 199 + 211), Mertens function(607) = 0, strictly non-palindromic number, also area code of Ithaca, New York
		The number 613 hangs from the rafters at Madison Square Garden in honor of legendary New York Knicks coach Red Holzman's 613 victories.
		659 prime number, Sophie Germain prime, sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Mertens function sets new low of -10 which stands until 661, highly cototient number, strictly non-palindromic number
	www.grohol.com /psypsych/600_(number) (1065 words)

	bigNumbers.nb
		Beyond a certain size, there are no names for large numbers, so you can create a new number and call it whatever you like.
		For calculations involving large numbers of things that may actually exist, a web site maintained by the National Aeronautics and Space Administration an excellent resource.
		An advanced student can readily explain the difference between “the largest number” and “the largest number that has a name.” When children ask, “What is the largest number?” they should be congratulated and encouraged to think of what adding 1 would do to the largest number.
	www.unl.edu /tcweb/fowler/analysesHTML/aboutBigNumbers (408 words)

	bash 2.05 mishandles redirection with large file descriptors
		But it mishandles '4294967297>' by treating it as if it were '>'.
		This causes output to be unexpectedly sent to the file 'x' rather than to standard output.
		NUMBER LESS_AND '-' { - redir.dest = 0L; + redir.dest = 0; $$ = make_redirection ($1, r_close_this, redir); }
	lists.gnu.org /archive/html/bug-bash/2001-04/msg00069.html (536 words)

	Section 5 (Site not responding. Last check: 2007-10-13)
		Since each Fermat Number is almost the square of the previous, the actual size of these grows rapidly as m increases, so that applying Pepin's Test for higher values of m is a massive task.
		There are Cullen numbers at n = 1, 141, 4713, etc., the current largest is at n = 481899 (Morii, Gallot, 1998), and there are Woodall numbers at n = 2, 3, 6, 30, 75, 81, 115, 123, etc., the current largest at n = 667071 (Toplic, Gallot, 2000).
		There exists and number S such that every sufficiently large integer is the sum of at most S primes.
	www.glasgowg43.freeserve.co.uk /pfaq5.htm (2216 words)

	Large Numbers -- Notes at MROB
		Their goal was to make it possible to derive every true theorem in number theory by starting with a set of axioms and a set of inference rules, and methodically applying all the inference rules to the axioms and existing theorems to create new theorems.
		But the number of 1's increases in a way that also depends in its value modulo 4, with the result that the value modulo 4 changes in a "chaotic" manner.
		If the number of terms is infinite, P has to be defined a different way, because the infinite regression symbolized by "..." is not allowed at the beginning of an infinite ordinal sum (for technical reasons).
	home.earthlink.net /~mrob/pub/math/ln-notes1.html (8124 words)

	Fermat Number -- from MathWorld (Site not responding. Last check: 2007-10-13)
		A current list of the known factors of Fermat numbers is maintained by Keller, and reproduced in the form of a
		Gardner, M. "Patterns in Primes are a Clue to the Strong Law of Small Numbers." Sci.
		Krízek, M.; Luca, F.; and Somer, L. Lectures on Fermat Numbers: From Number Theory to Geometry.
	archive.mayashastra.org /References/Mathematics/Fermat_Number.html (732 words)

	ISSUE 428
		number is an x or a z, then an x or a z shall
		number shall be extended to the specified number
		the constant, the unsigned number shall be padded to the left with zeros."
	www.boyd.com /1364_btf/report/full_pr/428.html (6121 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		%e A077232 8=d(6)=A000037(6)=3^2-1 (not in A003654) hence a(6)=3 and b(6)=1 are the smallest numbers satisfying a^2-8*b^2=+1.
		There are a finite number of expressions including n copies of n and various arithmetic operations.
		%F A110141 Number of terms in row n is A000041(n) (partition numbers).
	www.research.att.com:9000 /~njas/sequences/eisBTfry00013.txt (4288 words)

	Re: [OpenCA-Devel] CA Certificate serial number.
		On Thu, Mar 24, 2005 at 04:08:43PM +0100, Michael Bell wrote: > Date: Thu, 24 Mar 2005 16:08:43 +0100 > From: Michael Bell <[EMAIL PROTECTED]> > Subject: Re: [OpenCA-Devel] CA Certificate serial number.
		In the mean time, I think we could remedy situation by taking serial number for the self signed CA cert from the crypto/serial.
		Discover which products truly live up to the hype.
	www.mail-archive.com /openca-devel@lists.sourceforge.net/msg02279.html (219 words)

	Edit Issue 428 - GNU Gnatsweb (Site not responding. Last check: 2007-10-13)
		the number of bits in an integer type, meaning the largest number supported.
		> the number of bits in an integer type, meaning the largest number supported.
		I don't like the second half of this, after "at least 32".
	www.boydtechinc.com /cgi-bin/issueproposal.pl?cmd=changeclass&pr=428 (6121 words)

	Fermat number Details, Meaning Fermat number Article and Explanation Guide
		Fermat number Details, Meaning Fermat number Article and Explanation Guide
		Fermat number Guide, Meaning, Facts, Information and Description
		Page Contains Information, Facts Details or Explanation Guide About Fermat number
	www.e-paranoids.com /f/fe/fermat_number.html (937 words)

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