20080829, 14:30  #56  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
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20080829, 14:47  #57  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3·23·89 Posts 
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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
1011111111101_{2} Posts 
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20080907, 17:45  #60  
Aug 2006
3^{2}·5·7·19 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^{2}×5×7×19 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
2^{5} 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. 
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