mersenneforum.org possibly stupid question about winning the $100,000  User Name Remember Me? Password  Register FAQ Search Today's Posts Mark Forums Read  2005-09-10, 21:30 #1 jasong "Jason Goatcher" Mar 2005 350710 Posts possibly stupid question about winning the$100,000 Not understanding the proving math, but having a good memory, wouldn't calculating "primorial 1billion minus 1" technically create a record prime? Or is there some lawyer wording to prevent this? "I'm assuming I'm correct in the assumption that primorial x minus 1 is always prime. Primorial x means multiplying all the primes from 1 to x, correct? Last fiddled with by jasong on 2005-09-10 at 21:30
 2005-09-10, 21:42 #2 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Step 1 (always!): Look at small cases. Alex
2005-09-10, 22:21   #3
jasong

"Jason Goatcher"
Mar 2005

1101101100112 Posts

Quote:
 Originally Posted by akruppa Step 1 (always!): Look at small cases. Alex
I know it's correct for the first five. The square root of the sixth one(30029) is about 173, and I'm feeling lazy. Truthfully, I seem to remember that it's proven that primorial x minus 1 is prime, am I wrong?

 2005-09-10, 22:34 #4 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts >I know it's correct for the first five. 2*3*5*7-1 = 209 = 11*19 For the primorial n#, n#±1 has no prime divisor ≤n, but can very well have larger divisors. Alex Last fiddled with by akruppa on 2005-09-16 at 14:52
 2005-09-10, 22:40 #5 fetofs     Aug 2005 Brazil 2·181 Posts Other than that, there is another constraint: Calculating the primorial for 1 billion digit would actually involve knowing every other prime below it.
 2005-09-10, 22:55 #6 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts I read jasong's suggestion as 1000000000#-1, i.e. $\large \prod_{2\leq p\leq10^9\\p \textrm{ prime}} {p} \hspace{3}- 1$ Computing the primes <10^9 is quite easy, but the product will be pretty large. Alex (my TeX-fu is weak . This took way too long)
 2005-09-10, 23:18 #7 jasong     "Jason Goatcher" Mar 2005 350710 Posts Okay, I'm confused, am I right or wrong about the idea that primorial x minus 1 is prime? I seem to remember a proof, but...
 2005-09-10, 23:25 #8 rogue     "Mark" Apr 2003 Between here and the 23·19·43 Posts Check out http://primorialprime.home.comcast.net/. It is a search for primorial primes. You can clearly see that there are few primorials.
2005-09-10, 23:32   #9
jasong

"Jason Goatcher"
Mar 2005

66638 Posts

Quote:
 Originally Posted by rogue Check out http://primorialprime.home.comcast.net/. It is a search for primorial primes. You can clearly see that there are few primorials.
Okay, I apologize, although I would like to know where I got my false idea.

Okay, this goes in the bin along with the mentally ill delusion I used to have that Saddam Hussein and Bill Clinton were in cahoots. (Cahoots over what? I don't remember)

2005-09-10, 23:34   #10
jasong

"Jason Goatcher"
Mar 2005

1101101100112 Posts

Quote:
Originally Posted by akruppa
Quote:
 Originally Posted by jasong I know it's correct for the first five.
2*3*5*7-1 = 209 = 11*19

For the primorial n#, n#1 has no prime divisor ≤n, but can very well have larger divisors.

Alex
Sorry, I missed this.

Last fiddled with by jasong on 2005-09-10 at 23:37

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