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 2005-01-20, 21:27 #1 grandpascorpion     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?
 2005-01-20, 21:53 #2 Mystwalker     Jul 2004 Potsdam, Germany 14778 Posts Sounds like the Law of Small Numbers.
 2005-01-20, 22:17 #3 grandpascorpion     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.
2005-01-22, 08:26   #4
Yogi

Oct 2004

916 Posts

What about 2 + 1 is divisable by 3?

Quote:
 Originally Posted by grandpascorpion Does anyone know of other cases like this?
The only examples I know are 1459 and 2999 (checked through 2454587).

 2005-01-23, 14:00 #5 grandpascorpion     Jan 2005 Transdniestr 1F716 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
2005-01-23, 17:14   #6
Yogi

Oct 2004

118 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 n-th 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 n-value; there is no p(0))
Attached Files
 prim.zip (599 Bytes, 66 views)

 2005-01-25, 00:26 #7 grandpascorpion     Jan 2005 Transdniestr 503 Posts Thanks Yogi
 2005-02-06, 06:06 #8 Ken_g6     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?
2005-02-06, 06:41   #9
jinydu

Dec 2003
Hopefully Near M48

2×3×293 Posts

Quote:
 Originally Posted by Ken_g6 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?
Yes, but not all numbers of the form (n primorial) + 1 are prime because you can't rule out factors larger than n.

2005-02-10, 07:13   #10
maxal

Feb 2005

22×32×7 Posts

Quote:
 Originally Posted by Yogi What about 2 + 1 is divisable by 3? The only examples I know are 1459 and 2999 (checked through 2454587).
These are the only known such primes. See http://www.research.att.com/projects/OEIS?Anum=A058233

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