20080829, 14:30  #56  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Quote:


20080829, 14:47  #57  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3×11^{2}×17 Posts 
Quote:
f(x)=398x^2; x element of N To satisfy MiniGeek's requirement of total primes: f(x)=143x^2; x element of Z Last fiddled with by retina on 20080829 at 15:11 Reason: Forgot to specifiy the Z set 

20080829, 15:55  #58 
Feb 2008
2^{5} Posts 
I am obviously not communicating well. However you could have referred me to primes.utm.edu (as done by Cruelty) or Wikipedia or some other helpful web site. I am looking for "interesting" examples as listed on these web sites.
On the primes.utm.edu site Rudolf Ondrejka lists ten rare primes. One example he refers to as a beastly palindrome of the type (10^n 666)*10n2+1. Has it been proven that only 7 exist? Wikipedia, states that there is only one positive Genocchi prime; has this been proven? Last fiddled with by Housemouse on 20080829 at 15:56 
20080829, 16:03  #59  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1100000011011_{2} Posts 
Quote:


20080907, 17:45  #60  
Aug 2006
3×1,993 Posts 
Quote:
15/4 * (1/log(10^(2n2))) The sum of this from 2 to 3000 is 6.98, so having 7 from n = 2 to 3000 is pretty much what you'd expect. The expected number up to a million is 11.72, so it would be unusual if only 7 existed. In fact, since the harmonic series diverges, you'd naively expect an infinite number of such primes. MathWorld has "D. Terr (pers. comm., Jun. 8, 2004) proved that these are in fact, the only prime Genocchi numbers.". 

20080907, 18:08  #61 
Aug 2006
3×1,993 Posts 
To the original question: Of course there are uncountably many sets of primes (beth_1), a countable number of which sets are finite; but the question seems to be about intuitively 'interesting' sets of primes.
Toward that end I suggest my small compilation here: http://en.wikipedia.org/wiki/User:CR...special_primes 
20080911, 12:31  #62 
Feb 2008
40_{8} Posts 
Additional "interesting examples"
I found additional "interesting examples" at primes.utm.edu, under Rudolf Ondrejka's top ten.
Sometimes finding useful information using google is like looking for a needle in a hay stack. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is CEMPLLA 1.5 "the only software in the world capable of discovering" something? Not really.  CRGreathouse  Number Theory Discussion Group  51  20181216 21:55 
AouessareEl HaddouchiEssaaidi "test": "if Mp has no factor, it is prime!"  wildrabbitt  Miscellaneous Math  11  20150306 08:17 
Palindrome primes (a.k.a. Elementary S03E03 "Just a Regular Irregular")  Batalov  And now for something completely different  12  20141116 19:03 
PrimeRelated History: Leibniz' "Universal Language Based on Primes"  ewmayer  Math  10  20070302 12:47 
Would Minimizing "iterations between results file" may reveal "is not prime" earlier?  nitai1999  Software  7  20040826 18:12 