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 2003-08-06, 08:59 #1 Xyzzy     "Mike" Aug 2002 8,167 Posts Special whole numbers... List a whole number... The next poster has to say what makes that whole number special, and then he or she has to list a new one... (Please be clever and please try not to cheat too much!) Discussion about these numbers is encouraged, but keep the chain going! :) For example... 7
 2003-08-06, 09:00 #2 Xyzzy     "Mike" Aug 2002 816710 Posts 7 wonders of the ancient world... 50
 2003-08-06, 10:07 #3 Thomas   Jul 2003 Wuerzburg, Germany 23 Posts 50 States in the USA... 21
 2003-08-06, 10:29 #4 trif     Aug 2002 2·101 Posts 21 Blackjack 6
 2003-08-06, 11:32 #5 smh     "Sander" Oct 2002 52.345322,5.52471 29×41 Posts 6 the first perfect number 9
 2003-08-06, 12:51 #6 ET_ Banned     "Luigi" Aug 2002 Team Italia 113168 Posts 9 first odd square.(after 1) 42 ;)
 2003-08-06, 13:13 #7 dswanson     Aug 2002 C816 Posts 42 - Answer to the question of life, the universe, and everything. 101
 2003-08-06, 13:20 #8 ET_ Banned     "Luigi" Aug 2002 Team Italia 2·29·83 Posts 101 - dalmatians :D 101 - the first prime above 100 101 - the 101th Fibonacci number in binary notation 601
2003-08-06, 21:09   #9
ewmayer
2ω=0

Sep 2002
República de California

3×3,877 Posts

Quote:
 Originally Posted by ET_ 9 first odd square.(after 1) 42 ;)
A non-wink answer: the product of the first 3 primes in a Euclid-style sequence beginning with 2. This sequence is defined as "start with one or more distinct known primes. Take their product and add one. The result is either a new prime, or factors into a set of new primes. In either case, add the newly found prime or prime factors to your set of known primes and continue."

Beginning with just the smallest known prime, 2, we add one, to get 3, which is also prime.

2*3 + 1 = 7, which is again prime. The product of 2, 3 and 7 is 42.

A more interesting question is: will such a Euclid-type inductive sequence eventually yield ALL the primes? For instance, if we continue the particular sequence above, we get:

2*3*7 + 1 = 43, which is again prime.

2*3*7*43 + 1 = 1807 = 13*139.

2*3*7*13*43*139 + 1 = 3263443, which is prime.

2*3*7*13*43*139*3263443 + 1 = 10650056950807 = 547*607*1033*31051.

It's pretty easy to show that the Euclid sequence starting with 2 and 3 never yields a number divisible by 5, so the answer to the above question is no. So we refine the question: is there *any* Euclid sequence starting with a finite number of primes which yields all the primes?

Either that, or 42 is Luigi's age. :)

 2003-08-07, 20:47 #10 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 641 Posts 601 is the 110th prime, the divisors of 110 (sans 110) add up to 106, which is 601 backwards 539
2003-08-07, 23:34   #11
ewmayer
2ω=0

Sep 2002
República de California

3×3,877 Posts

Quote:
 Originally Posted by TravisT 539
The number of the statutory instrument governing production of fresh meat products in Great Britain:

http://www.hmso.gov.uk/si/si1995/Uksi_19950539_en_1.htm

5171655946

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