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Topic: largest prime number found: 9.1 million digits long
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Reality. Bites.
rabble-rouser
Babbler # 6718
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posted 04 January 2006 10:58 AM
quote:
Originally posted by Hephaestion:
(I'd put it in the post, but it'd cause absolutely bitchin' side-scroll!)
Assuming a typical 3mm per character (depending on screen size and resolution), it would cause 2.7 km of side scroll, similar to oh, any Toronto Star link.
From: Gone for good | Registered: Aug 2004
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Yukoner
rabble-rouser
Babbler # 5787
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posted 04 January 2006 04:40 PM
quote:
Originally posted by RealityBites:
You're the one stereotyping vampires. The Count is well known for his love of numbers but it's pure prejudice for you to assume that has anything to do with his vampirility. If I see a blue-furred monster with hypoglycemia self-medicating with cookies, do I assume all share his problem? Of course not.
...some of my best friends are vampires...
From: Um, The Yukon. | Registered: May 2004
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Sven
rabble-rouser
Babbler # 9972
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posted 04 January 2006 07:49 PM
quote:
Originally posted by JimmyBrogan:
Theoretically wouldn't the set of all primes be infinite?
quote:
Originally posted by Agent 204:
Yeah, that's old news- around 2300 years old, in fact.
Are there different definitions of "infinity"? If the set of all prime numbers is "infinite" and if the set of all whole numbers is also "infinite", it would seem that the former quantum of "infinite" would be smaller than the latter quantum of "infinite" because the former quantum of "infinite" would not include non-prime whole numbers. So, doesn't that necessarily mean that the word "infinite" has more than one meaning? I'm no mathematician or logician but this topic and the exchange between JimmyBrogan and Agent 204 got me thinking about that question.
From: Eleutherophobics of the World...Unite!!!!! | Registered: Jul 2005
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fast_twitch_neurons
rabble-rouser
Babbler # 10443
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posted 04 January 2006 08:32 PM
The smallest known infinity is the aleph-0 cardinality. It's any infinity which can be put into a one-to-one corresponce with the natural numbers (1,2,3,4...). The even numbers, the fractions, and the primes are all sets of the same cardinality as the integers. The even numbers, we have 2 corresponding to one, 4 corresponds to 2, 6 corresponds to 3, and so on and so forth, and as such since we have a 1:1 correspondence between the set of positive numbers and the set of even positive numbers, they are of the same infinity.
From: Montreal | Registered: Sep 2005
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Agent 204
rabble-rouser
Babbler # 4668
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posted 04 January 2006 08:33 PM
quote:
Originally posted by Sven:
Are there different definitions of "infinity"? If the set of all prime numbers is "infinite" and if the set of all whole numbers is also "infinite", it would seem that the former quantum of "infinite" would be smaller than the latter quantum of "infinite" because the former quantum of "infinite" would not include non-prime whole numbers. So, doesn't that necessarily mean that the word "infinite" has more than one meaning? I'm no mathematician or logician but this topic and the exchange between JimmyBrogan and Agent 204 got me thinking about that question.
No, but yes. Confused yet? Your observation about primes and natural numbers (or even and natural numbers, for that matter) is a good one. The way mathematicians deal with it is to say that two sets have the same cardinality (i.e. the same number of members) if, and only if, they can be put in one-to-one correspondence with each other. This seems obvious with finite sets, but it gives interesting results with infinite ones. Suppose we were to line up the set of natural numbers with the set of primes: 1 2 3 4 5 6 7 ...
2 3 5 7 11 13 17 ... Since you can always add a new prime to the bottom list for any new natural number in the top list, the two sets are in one-to-one correspondence with each other, and are thus equivalent. So, oddly enough, is the set of all rationals. Such sets are called "countably infinite", since natural numbers are "counting" numbers (not that any of us would have time to do the counting!) The point where it gets really confusing is when dealing with the real numbers. Georg Cantor showed that the set of all real (i.e. rational plus irrational) numbers cannot be put in one-to-one correspondence with the natural numbers- they are "uncountably infinite", i.e. there are more reals than integers! What hasn't been determined- and can't be unless and until established set theory is expanded upon- is whether there is any infinite set intermediate in size between the integers and the reals... but at this point my head starts spinning too.
From: home of the Guess Who | Registered: Nov 2003
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M. Spector
rabble-rouser
Babbler # 8273
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posted 04 January 2006 08:41 PM
The number of primes is also of the same "cardinality" as the integers. Since there is an infinite number of primes, we can start numbering them, from the smallest to the largest. The first prime number (let's call it P1) is 2; the second prime number (P2) is 3; P3 = 5, P4 = 7, etc. So each prime has its own unique "P number", and each integer we tack onto a P represents a unique prime. So, there is a one-to-one correspondence between the integers and the primes. That means the infinity of integers is the same as the infinity of primes. [ 05 January 2006: Message edited by: M. Spector ]
From: One millihelen: The amount of beauty required to launch one ship. | Registered: Feb 2005
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M. Spector
rabble-rouser
Babbler # 8273
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posted 10 January 2006 07:07 PM
Sunday, January 22, 2006 - 3 pm
Macleod Auditorium, Medical Sciences Bldg.
University of Toronto, 1 King's College Circle
(Queen's Park Subway Station)Infinity: The Most Fascinating of All Ideas Miroslav Lovric, PhD, Dept. of Mathematics and Statistics, McMaster University Infinity has many faces. Sometimes, we perceive it as a "number" larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at seven. Infinity for Van Gogh was a vast, unending plane, on which imagination is given free rein. For the Moors, creators of exquisite mosaics and patterns whose sophistication has never been surpassed, infinity was a repetition of a single artistic motif. This lecture will sketch a cultural history of infinity, spanning thousands of years including the amazingly straightforward concepts developed by mathematician Georg Cantor, that form the basis of our modern understanding of infinity. Cantor had the courage to look infinity into its eyes, and what he saw deeply shocked him. "I see it, but I do not believe it" he exclaimed as his discoveries, shook mathematics to its core. Cantor died in a mental institution. What drove him to insanity? Does infinity really exist? If so, where can we find it? Is our universe large enough to encompass infinity? Further reading: The Mystery of the Aleph, Washington Square Press, 2000, ISBN 0-7434-3399-6, Oxford University Press 1987, ISBN 0-19-283202-6 Clifford Pickover, Keys to Infinity, John Wiley and Sons, 1995, 1SBN 0-171-11857-5 Co-sponsored by The Fields Institute for Research in Mathematical Sciences [ 10 January 2006: Message edited by: M. Spector ]
From: One millihelen: The amount of beauty required to launch one ship. | Registered: Feb 2005
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