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-   -   Special whole numbers... (https://www.mersenneforum.org/showthread.php?t=935)

 Xyzzy 2003-08-06 08:59

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

 Xyzzy 2003-08-06 09:00

7 wonders of the ancient world...

50

 Thomas 2003-08-06 10:07

50 States in the USA...

21

 trif 2003-08-06 10:29

21 Blackjack

6

 smh 2003-08-06 11:32

6 the first perfect number

9

 ET_ 2003-08-06 12:51

9 first odd square.(after 1)

42 ;)

 dswanson 2003-08-06 13:13

42 - Answer to the question of life, the universe, and everything.

101

 ET_ 2003-08-06 13:20

101 - dalmatians :D
101 - the first prime above 100
101 - the 101th Fibonacci number in binary notation

601

 ewmayer 2003-08-06 21:09

[quote="ET_"]9 first odd square.(after 1)

42 ;)[/quote]

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. :)

 Orgasmic Troll 2003-08-07 20:47

601 is the 110th prime, the divisors of 110 (sans 110) add up to 106, which is 601 backwards

539

 ewmayer 2003-08-07 23:34

[quote="TravisT"]539[/quote]

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