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Topic: Large numbers

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	Large numbers - Wikipedia, the free encyclopedia
		Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions.
		The first number is much larger than the second, due to the larger height of the power tower, and in spite of the small numbers 1.1 (however, if these numbers are made 1 or less, that greatly changes the result).
		With extremely large numbers, the relative error may be large, yet there may still be a sense in which we want to consider the numbers as "close in magnitude".
	en.wikipedia.org /wiki/Large_numbers (2734 words)

	Names of large numbers - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-08-19)
		Nevertheless, large numbers have an intellectual fascination and are of mathematical interest.
		In science, since the 1800s, numbers have been written using the familiar "scientific notation", in which powers of ten are expressed as a ten with a numeric superscript, e.g.
		When a number represents a measurement rather than a count, SI prefixes are used; one says "femtosecond", not "one quadrillionth of a second." In some cases, specialized very large units are used, such as the astronomer's parsec and light year.
	www.fridley.us /project/wikipedia/index.php/Quintillion (2021 words)

	Large Prime Numbers
		In mathematical notation, the new prime number is expressed as 2^1257787-1, which denotes two, multiplied by itself 1,257,787 times, minus one.
		Numbers expressed in this form are called Mersenne prime numbers after Marin Mersenne, a 17th century French monk who spent years searching for prime numbers of this type.
		The new perfect number generated with the new Mersenne prime is the 34th known perfect number and has 757,263 digits.
	www.isthe.com /chongo/tech/math/prime/prime_press.html (877 words)

	Large numbers - (Site not responding. Last check: 2007-08-19)
		If the height is too large to write out the whole power tower, a notation like $(10\uparrow)^{183}(3.12*10^6)$ can be used, where $(10\uparrow)^{183}$ denotes a functional power of the function $f(n)=10^n$ (the function also expressed by the suffix "-plex" as in googolplex, see the Googol family).
		The "order of magnitude" of a number (on a larger scale than usually meant), can be characterized by the number of times (say n) one has to take the $log_{10}$ to get a number between 1 and 10.
		In a number like $10^{\,\!6.2 \times 10^3}$ , with the 6.2 the result of proper rounding, the true value of the exponent may be 50 less or 50 more.
	psychcentral.com /psypsych/Large_number (2940 words)

	Names for Large Numbers
		The English names for large numbers are coined from the Latin names for small numbers n by adding the ending -illion suggested by the name "million." Thus billion and trillion are coined from the Latin prefixes bi- (n = 2) and tri- (n = 3), respectively.
		In science, the names of large numbers are usually avoided completely by using the appropriate SI prefixes.
		The googolplex (1 followed by a googol of zeroes) is far larger than any of the numbers discussed here.
	www.unc.edu /~rowlett/units/large.html (670 words)

	Factoring Large Numbers
		Finding the prime factors of large numbers was considered an interesting, but purely theoretical problem until in 1978 Rivest, Shamir and Adleman (RSA) proposed to use the near-impossibility of reconstructing the prime factors from the product of two large prime numbers as an encryption technique to protect sensitive information.
		The question how large the constituting prime numbers should be chosen in order to guarantee the RSA-encryption to be `safe' depends on the time needed by the most advanced computers to find these numbers from their product.
		A third method, called the Number Field Sieve (NFS) (J.M. Pollard, 1993), is expected to be more efficient for general numbers than QS, and finding out the cross-over point between NFS and QS (presently around 105 decimal digits) is the subject of intensive current research at CWI and elsewhere.
	www.ercim.org /publication/Ercim_News/enw22/large-numbers.html (612 words)

	Large Numbers
		But historically, a large number was whatever the prevailing culture deemed it to be an intrinsically circular definition.
		Somewhat above the googol lie numbers that present a sharp challenge to practitioners of the art of factoring: the art of breaking numbers into their prime factors, where primes are themselves divisible only by 1 and themselves.
		LARGE NUMBERS- such as the 100-digit, or googol-size, ones running across the tops of these pages - have become more accessible over time thanks to advances in computing.
	www.fortunecity.com /emachines/e11/86/largeno.html (3119 words)

	The Law of Large Numbers (Site not responding. Last check: 2007-08-19)
		The difference between the number of successes and the number of trials times the chance of success in each trial (the expected number of successes) tends to grow as the number of trials increases.
		The distribution of the number of successes in n independent trials with probability p of success in each trial is Binomial, with parameters n and p.
		The controls on this applet let you change the number of trials, the probability of success in each trial, and toggle between viewing either the difference between the number of successes and the expected number of successes, or the difference between the percentage of successes and the probability of success in each trial.
	www.stat.berkeley.edu /~stark/Java/Html/lln.htm (164 words)

	Large Numbers at MROB (Site not responding. Last check: 2007-08-19)
		Almost all numbers that are easy to make simple statements about (such as which of two numbers is larger) can be put into the class system.
		Class-1 numbers are those that are small enough to be perceived as a bunch of objects seen directly by the human eye.
		Googol is a class-2 number, as are the various large prime numbers used in cryptography, all of the known Perfect numbers, the Fermat numbers with known factorization, etc. All of the large physical constants like 6.02×10
	home.earthlink.net /~mrob/pub/math/largenum.html (3896 words)

	Kids.net.au - Encyclopedia History of large numbers - (Site not responding. Last check: 2007-08-19)
		In the Western world specific number names for larger numbers did not come into common use until quite recently.
		However, the Indians, who also invented the positional number system and the zero, were much more advanced in this aspect than all the other civilisations of Antiquity and the Middle Ages.
		One interresting point in using large numbers is the confusion on the term Billion and Milliard in many countries.
	www.kidsseek.com /encyclopedia-wiki/hi/History_of_large_numbers (434 words)

	Law of large numbers: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-08-19)
		The phrase "law of large numbers" is also sometimes used to refer to the principle that the probability of any possible event (even an unlikely one) occurring at least once in a series increases with the number of events in the series.
		A consequence of the weak law of large numbers is the asymptotic equipartition property[For more facts and a topic of this subject, click this link].
		Proofs of the above weak and strong laws of large numbers are rather involved.
	www.absoluteastronomy.com /encyclopedia/l/la/law_of_large_numbers.htm (1683 words)

	Large numbers
		Reading large numbers in Japanese may be awkward if your native language uses a system based on one thousand.
		To read large numbers in Japanese, divide them into four-digit groups, and read the groups separately and add appropriate units.
		The units of big numbers affect the phonemes of the last mora of the preceding four-digit group.
	www.sf.airnet.ne.jp /ts/japanese/largenumber.html (192 words)

	Hussman Funds - Weekly Market Comment: October 25, 2004 - Law of Large Numbers
		That said, the law of large numbers suggests that short-term returns should eventually begin to average out toward the long-term average if all is well.
		Notice that the law of large numbers requires the samples to be “independent.” Following a particular investment approach over numerous time periods would qualify those samples as being reasonably independent, for example.
		Since we also know that there is no large or simple correlation between market movements in the recent past and market movements in the near future, it follows that the part of advisory sentiment explained by past movements is just plain uninformative as well.
	www.hussmanfunds.com /wmc/wmc041025.htm (2136 words)

	The Largest Known Primes
		The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
		Because the way the largest numbers N are proven prime is based on the factorizations of either N+1 or N-1, and for Mersennes the factorization of N+1 is as trivial as possible (a power of two).
		These are the easiest type of number to check for primality on a binary computer so they usually are also the largest primes known.
	primes.utm.edu /largest.html (1151 words)

	Law of Truly Large Numbers
		The law of truly large numbers says that with a large enough sample many odd coincidences are likely to happen.
		The number is actually likely to be larger, since we tend to dream about things that legitimately concern or worry us, and the data of dreams is usually vague or ambiguous, allowing a wide range of events to count as fulfilling our dreams.
		Given the fact that there are billions of people and the possible number of meaningful coincidences is millions of billions, it is inevitable that many people will experience some very weird and uncanny coincidences every day.
	skepdic.com /lawofnumbers.html (1327 words)

	Large Numbers
		If you start with 30,000 and you were to move the decimal place to the left until it was next to the 3, which is the first non-zero digit in the number, you would have moved the decimal four places.
		The number of places the decimal has to move becomes the exponent for the 10.
		Thirty-four thousand can be written as 3.4 times 10,000, which in turn can be written as 3.4 times 10 to the fourth.
	dl.clackamas.cc.or.us /ch104-02/large.htm (226 words)

	Math Forum: Ask Dr. Math FAQ: Large Numbers and Infinity
		Well, 1,000,000,000 (1 billion) can't be the largest number because 1 billion + 1 is bigger - but that is true for any number you pick.
		There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it's not a number at all.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /dr.math/faq/faq.large.numbers.html (665 words)

	Problem F - Factoring Large Numbers (Site not responding. Last check: 2007-08-19)
		One of the central ideas behind much cryptography is that factoring large numbers is computationally intensive.
		In this context one might use a 100 digit number that was a product of two 50 digit prime numbers.
		Each positive number from the input must be factored and all factors (other than 1) printed out.
	acm.uva.es /p/v103/10392.html (164 words)

	Names for large numbers
		All possible large number words, sorted by word length.
		This is the most concise way and the most reproducible way to represent large numbers.
		A silly, but most amusing way, to represent large numbers is by their more or less official 'Latin' representation as is done here.
	home.hetnet.nl /~vanadovv/BignumbyN.html (562 words)

	Memorise Large Numbers - Maths-Alphabet Trick to memorize numbers
		we can easily remember peoples faces or colors but numbers are very hard to memorize because they are so hard to associate,our brain thinks with pictures not with numbers.
		That way could work the same way as the numbers, you could forget a word or get confused which letter is for which number.
		I can never remember names, but numbers seem to stick with me. I figure if everyones name was actually a number, I'd never forget anyones name..
	www.trap17.com /index.php/memorise-large-numbers_t33899.html (840 words)

	Understanding Large Numbers - Volume 18 No. 1 - Fall 2003 - Rethinking Schools Online
		Imagining a billion boggles my mind, whether I'm trying to fathom that number of galaxies swirling around the universe or the number of H 2 O molecules in a drop of water.
		Teaching about these matters provides students an opportunity to improve their understanding of large numbers, and even more importantly, understand the power of math in debates about the future of our communities and world.
		After timing the counting of a series of very large numbers, we estimated it would take about three seconds a number if we were to count to a billion — leading us to conclude it would take almost 96 years to count to a billion.
	www.rethinkingschools.org /archive/18_01/numb181.shtml (1298 words)

	Math Forum - Ask Dr. Math Archives: Elementary Large Numbers (Site not responding. Last check: 2007-08-19)
		We are a 3/4 class, studying large numbers.
		I just read an article about the "last finite number", and I was wondering whether such a number could possibly exist.
		In Rowlett's site for naming large numbers, he seems to take every American prefix and bump its meaning by one to get the corresponding Greek-based prefix.
	mathforum.org /library/drmath/sets/elem_large_numbers.html (549 words)

	Large Numbers
		The other common practice is to assign a name with a latinized prefix for N to the number 10^(6N).
		Well, one way of making extremely large finite numbers is to repeat this process to silly extremes.
		By ``more'', we mean no matter how one chooses to pair off real numbers with natural numbers, there will always be some real numbers which are not paired off.
	www.sci.wsu.edu /math/faculty/hudelson/moser.html (736 words)

	Archimedes
		The first really large number to surface in science was related to atoms and molecules.
		For about 2000 years large numbers were ignored--the great mathematician Gauss said infinity should only be used as "a way of speaking" and not as a mathematical value.
		A very large number was concocted in 1938 by Columbia University mathematician Edward Kasner and named after a word used by his 9 year old nephew.
	mooni.fccj.org /~ethall/archmede/archmede.htm (1010 words)

	LARGE NUMBERS
		Previously they were separated into groups of six, then came into use the modern grouping of three digits.
		As can be seen, the name of a large number is:
		- in the European system: when the number of zeros is divisible by 6, the Latin name of the quotient of such division, plus the suffix illion.
	www.arlindo-correia.com /040705.html (205 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 (8484 words)

	Prime Numbers and Factoring (Site not responding. Last check: 2007-08-19)
		This page is a collection of links related to prime numbers and factoring of very large numbers.
		This FAQ from RSA Labs surveys a modern topic which may be applied to factoring very large numbers using techniques reminiscent of quantum mechanics.
		The New RSA Factoring Challenge RSA is offering prizes for factoring large numbers suitable for encryption keys.
	www.ontko.com /~rayo/primes (561 words)

	Online Conversion - Large Numbers
		There is not a standard naming scheme for numbers over a million, and different countries call numbers different things.
		The list is a bit difficult to read, sorry, I couldn't write out the numbers, since a number with 600 zeros after it would take up quite a bit of room.
		There are other names of numbers that are not part of any standard number system.
	www.onlineconversion.com /large_numbers.htm (195 words)

	Law of large numbers Info - Encyclopedia WikiWhat.com (Site not responding. Last check: 2007-08-19)
		In probability theory, the weak law of large numbers states that if X
		Chebyshev's inequality is used to prove this result.
		A consequence of the weak law of large numbers is the asymptotic equipartition property.
	wikiwhat.com /encyclopedia/l/la/law_of_large_numbers.html (191 words)

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