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![[Post New]](/templates/default/images/icon_minipost_new.gif) 22 Apr 2008 22:58:09 IST
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Hey ppl
Prove that no. of prime numbers is infinite. Some of u may already knw this though. Rates assured.
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22 Apr 2008 23:04:28 IST
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Let the no. of prime no.s be finite 'coz the largest prime no. is known.But super-computers are workin' all the time to find the next largest prime and the list is goin' on increasing.
So the no of prime no.s is infinite.
Hence, proved!!!
~Cheerio!!!
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Talk less work more!! {To be simplistic and 2 gain respect}
Eat less work more!!! {To "build" ur body}
Work less Do more!!! {2 make ur life big}
don't get scared !!!
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22 Apr 2008 23:07:48 IST
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Really i dint expect this for an answer !!!
Good one though buddy, but u overlooked something.
I asked u to prove it.
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23 Apr 2008 16:28:21 IST
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Is noone able to prove this ?
Come on GoIITians !!!
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23 Apr 2008 16:37:08 IST
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Consider any finite set of primes. Multiply all of them together and add one . The resulting number is not divisible by any of the primes in the finite set we considered, because dividing by any of these would give a remainder of one. Because all non-prime numbers can be decomposed into a product of underlying primes, then either this resultant number is prime itself, or there is a prime number or prime numbers which the resultant number could be decomposed into but are not in the original finite set of primes. Either way, there is at least one more prime that was not in the finite set we started with. This argument applies no matter what finite set we began with. So there are more primes than any given finite number.
this method of proof was given by euclid
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all the best ... |
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23 Apr 2008 16:39:17 IST
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here's a simple proof due to Euclid (or was it Euler? dnt remember)
Let n be the largest prime. Consider the number n! + 1. It is not divisible by any number upto n since all numbers upto n are factors of n! so they wont be factors of n! + 1.
This means that n!+1 must (1) either have some prime factor greater than n or (2) be a prime itself.
In any case, the assumption that n is the largest prime is contradicted.
That completes ur proof :)
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23 Apr 2008 16:39:47 IST
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srry arpan didnt see u had posted the solution already 
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23 Apr 2008 16:43:25 IST
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Very good guyz.
I expected the same answer. Nice to know thr r brilliant ppl out here ! Not that those who dint answer r not brilliant....
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