20050120, 21:27  #1 
Jan 2005
Transdniestr
503 Posts 
Factors of primorials
Just curious,
The lowest factor of 2* 3 * 5 * 7 * 11 * 13 * 17 +1 is 19, the next prime after 17. Does anyone know of other cases like this? 
20050120, 21:53  #2 
Jul 2004
Potsdam, Germany
1477_{8} Posts 
Sounds like the Law of Small Numbers.

20050120, 22:17  #3 
Jan 2005
Transdniestr
503 Posts 
Maybe a law of one?
I have checked thru 227. This is the only guy I have seen so far. 
20050122, 08:26  #4  
Oct 2004
9_{10} Posts 
What about 2 + 1 is divisable by 3?
Quote:


20050123, 14:00  #5 
Jan 2005
Transdniestr
1F7_{16} Posts 
I was thinking of factors only and missed the obvious I guess.
Thanks for the other values. Could you point me to the link where you saw them? Grandpa 
20050123, 17:14  #6 
Oct 2004
3^{2} Posts 
Not really, since I used a self written program. I attached it (in case you want to see it). I know it's not optimal, but it works.
And before I forget: You'll need NTL (Number theoretic library from Victor Shoup; free) if you want to compile it. I couldn't attach the zipped (cygwin) .exe, since it's still too large. Usage: prim <n> where n denotes the nth prime, so you'd get the result (p(1)# + 1) % p(2) = 0 if you run it with "prim 0". (It always skips the first nvalue; there is no p(0)) 
20050125, 00:26  #7 
Jan 2005
Transdniestr
503 Posts 
Thanks Yogi

20050206, 06:06  #8 
Jan 2005
Caught in a sieve
2×197 Posts 
This sounds alot like Euclid's proof that there are infinitely prime numbers. I believe it says that n primorial + 1 is not divisible by any prime smaller than n, correct?

20050206, 06:41  #9  
Dec 2003
Hopefully Near M48
2·3·293 Posts 
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20050210, 07:13  #10  
Feb 2005
2^{2}×3^{2}×7 Posts 
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