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 2008-08-19, 19:34 #1 Housemouse     Feb 2008 2016 Posts "Rare" Primes I am looking for "rare" prime numbers. For purposes of this tread a prime number is rare if there are 10 or less known examples. Even if it is believed that there is an infinate number of primes of a partiocular type; it is rare if there are 10 or less known examples. Even primes n n=2 Generalized Fermat 10^2^n+1 n=1 Subfactorial !n n=2 Perfect number -1; n is a perfect number n=6 Sequential prime of type (1234567890)n1 n=17, 56 Subfactorial +1; !n+1 n=2, 3 Type: n^n^n +1 n=1, 2 Wilson primes; (n-1)!+1 is divisible by n^2 Subfactorial - 1; !n-1 n= 5, 15, 17 Type: n^n+1 n=1, 2, 4 Double Mersenne; 2^n-1; where n is a Mersenne prime n=2, 3, 5, 7 Perfect number +1; where n is a perfect number n= 6, 28, 496, 137,438,691,328 Fermat prime; 2^n+1 n=0, 1, 2, 3, 4 Repunit containing only decimal digit 1; n= number of digits n=2, 19, 23, 317, 1,031
2008-08-19, 19:50   #2
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

22×367 Posts

Quote:
 Originally Posted by Housemouse I am looking for "rare" prime numbers. For purposes of this tread a prime number is rare if there are 10 or less known examples. Even if it is believed that there is an infinate number of primes of a partiocular type; it is rare if there are 10 or less known examples.
Every prime is rare: p is a prime then p is rare because it is only the solution of the equation x-p=0.

 2008-08-19, 20:40 #3 Housemouse     Feb 2008 25 Posts All primes Rare Is everyone from Hungary a sarcastic moron?
 2008-08-19, 20:54 #4 Cruelty     May 2005 23×7×29 Posts Have you tried looking here? BTW: I'm from Poland
2008-08-19, 22:54   #5
ewmayer
2ω=0

Sep 2002
República de California

3×3,877 Posts

Quote:
 Originally Posted by Housemouse Is everyone from Hungary a sarcastic moron?
LOL - allow me to try to inject a bit of international diplomacy with a mathematical flavor, by saying only that

"Not all sarcastic morons are from Hungary."

And that is all my government [which is not Hungarian, and has no special interest in the Goulash markets] has authorized me to say on the matter.

Last fiddled with by ewmayer on 2008-08-20 at 16:28 Reason: Removed stray text caused by a cosmic-ray-cascade of sarcastic muons

 2008-08-19, 22:56 #6 Housemouse     Feb 2008 25 Posts Have you looked here? Thank you for your tip!
 2008-08-20, 03:03 #7 Jens K Andersen     Feb 2006 Denmark E616 Posts As hinted by a not entirely moronic Hungarian, it strongly depends on which "types" you allow. http://primepuzzles.net/puzzles/puzz_225.htm has some possibilities. It's easy to construct rare prime forms by picking a quickly growing function with one or a few early primes. You mention Generalized Fermat 10^2^n+1, but there is no base b with more than 7 known primes b^2^n+1, and finding one with more than 10 looks very hard. The record is 7 for b=2072005925466 at http://primepuzzles.net/puzzles/puzz_399.htm If you want relatively notable named forms then some candidates are at http://en.wikipedia.org/wiki/List_of_prime_numbers (look for comments like "only known"). In addition to your list of proven repunit primes, there are known probable primes for n = 49081, 86453, 109297, 270343. There is no known Wall-Sun-Sun prime although infinitely many are expected to exist.
2008-08-20, 11:37   #8
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by Housemouse Is everyone from Hungary a sarcastic moron?
The reply to your post was accurate. "rare prime" is a poorly conceived
notion at best because as the reply shows it is TRIVIAL to construct
subsets of the integers containing only finitely many
primes under according to some rule. I am afraid that YOUR original
question shows that you are the moron. It shows a total lack of
mathematical understanding.

2008-08-20, 14:31   #9

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

Quote:
 Originally Posted by R.D. Silverman I am afraid that YOUR original question shows that you are the moron. It shows a total lack of mathematical understanding.

The original question's appropriate uses of the mathematical terms "Generalized Fermat", "Subfactorial !n", "Wilson primes", "Double Mersenne", "Fermat prime", and "Repunit" are unlikely to have been composed by someone with a "total lack of mathematical understanding".

Are you genuinely unable to discern, or at least politely respond to, the intent behind awkward wordings of mathematically-related postings? Or is it instead a matter of using this forum to vent anger that might otherwise, and less desireably, be expressed elsewhere in your life?

Last fiddled with by cheesehead on 2008-08-20 at 14:40

2008-08-20, 15:18   #10
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by cheesehead Perhaps your fear has clouded your reasoning, professor. The original question's appropriate uses of the mathematical terms "Generalized Fermat", "Subfactorial !n", "Wilson primes", "Double Mersenne", "Fermat prime", and "Repunit" are unlikely to have been composed by someone with a "total lack of mathematical understanding". Are you genuinely unable to discern, or at least politely respond to, the intent behind awkward wordings of mathematically-related postings? Or is it instead a matter of using this forum to vent anger that might otherwise, and less desireably, be expressed elsewhere in your life?
I am not the one who labelled the response to the original question
as coming from a moron.

And knowing the NAME of something is not the same as understanding it.
(A paraphrased quote from Richard Feynman). The fact that the O.P.
knows the names of a few objects is not an indication that he understands
mathematics.

The original query, as posed, used vague English words (e.g. rare prime) to
try to convey some mathematical idea. Mathematics is a domain of
knowledge in which it is possible to state PRECISELY what is intended.
The fact that the original poser used vague language and gave a very
poorly posed question is what makes clear that he lacks understanding of
mathematics.

The first response to the problem was a totally correct and precise
response to WHAT WAS ASKED. And then the O.P. labelled the
response as coming from a moron.

I notice that you failed to chide the O.P. for his response. Can you
say "double standard"??

2008-08-20, 18:14   #11
biwema

Mar 2004

17D16 Posts

Quote:
 Originally Posted by Jens K Andersen It's easy to construct rare prime forms by picking a quickly growing function with one or a few early primes. You mention Generalized Fermat 10^2^n+1, but there is no base b with more than 7 known primes b^2^n+1, and finding one with more than 10 looks very hard. The record is 7 for b=2072005925466 at http://primepuzzles.net/puzzles/puzz_399.htm
Maybe there is even a Generalized Fermat with more than 7 primes in the range b<10^15 or so. The sequence above assumes that n=0..6 of b^2^n+1 is prime. Maybe there is a generalized Fermat which has more than 7 primes that are not consecutive. For example if n=0,1,2,3,4,5,7,8 is prime.
The probability of that szenario is still pretty small.

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