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Old 2005-09-10, 21:30   #1
jasong
 
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"Jason Goatcher"
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Default 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
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Old 2005-09-10, 21:42   #2
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Step 1 (always!): Look at small cases.

Alex
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Old 2005-09-10, 22:21   #3
jasong
 
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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?
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Old 2005-09-10, 22:34   #4
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>I know it's correct for the first five.

2*3*5*7-1 = 209 = 11*19

For the primorial n#, n#ยฑ1 has no prime divisor โ‰คn, but can very well have larger divisors.

Alex

Last fiddled with by akruppa on 2005-09-16 at 14:52
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Old 2005-09-10, 22:40   #5
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Other than that, there is another constraint: Calculating the primorial for 1 billion digit would actually involve knowing every other prime below it.
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Old 2005-09-10, 22:55   #6
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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)
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Old 2005-09-10, 23:18   #7
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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...
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Old 2005-09-10, 23:25   #8
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Check out http://primorialprime.home.comcast.net/. It is a search for primorial primes. You can clearly see that there are few primorials.
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Old 2005-09-10, 23:32   #9
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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)
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Old 2005-09-10, 23:34   #10
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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#ฑ1 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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