possibly stupid question about winning the $100,000

jasong · 2005-09-10, 21:30

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?

akruppa · 2005-09-10, 21:42

Step 1 (always!): Look at small cases.

Alex

jasong · 2005-09-10, 22:21

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?

akruppa · 2005-09-10, 22:34

>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

fetofs · 2005-09-10, 22:40

Other than that, there is another constraint: Calculating the primorial for 1 billion digit would actually involve knowing every other prime below it.

akruppa · 2005-09-10, 22:55

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)

jasong · 2005-09-10, 23:18

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...

rogue · 2005-09-10, 23:25

Check out http://primorialprime.home.comcast.net/. It is a search for primorial primes. You can clearly see that there are few primorials.

jasong · 2005-09-10, 23:32

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)

jasong · 2005-09-10, 23:34

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.

2005-09-10, 21:30	#1
jasong "Jason Goatcher" Mar 2005 6663₈ 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, 22:34	#4
akruppa "Nancy" Aug 2002 Alexandria 100110100011₂ Posts	>I know it's correct for the first five. 2357-1 = 209 = 1119 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

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Stupid question reloaded	LaurV	Information & Answers	14	2015-06-18 23:37
There is -no- such thing as a stupid question?	Uncwilly	Lounge	19	2013-03-07 04:44
Possibly stupid question about porting games to Linux.	jasong	Linux	4	2006-12-23 21:24
Possibly stupid question about PRP.	Biggles	Prime Sierpinski Project	3	2006-02-07 22:50
Stupid Question	fropones	Math	2	2003-05-28 00:44

2005-09-10, 21:42	#2
akruppa "Nancy" Aug 2002 Alexandria 4643₈ Posts	Step 1 (always!): Look at small cases. Alex

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 3·7·167 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 2·59² Posts	Check out http://primorialprime.home.comcast.net/. It is a search for primorial primes. You can clearly see that there are few primorials.