20080204, 22:12  #1 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Primes mod 4
Are they as likely to ==1 as ==3?
PS thought I'd ask here rather than the proper maths thread to avoid embarrassment 
20080204, 22:24  #2 
May 2003
60B_{16} Posts 
Yes and no. ;)
What do you mean by "as likely"? Last fiddled with by ZetaFlux on 20080204 at 22:24 
20080204, 22:27  #3 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Are there the ~same number of each below 100M?
Last fiddled with by davieddy on 20080204 at 22:28 
20080204, 22:33  #4 
(loop (#_fork))
Feb 2006
Cambridge, England
1100011101000_{2} Posts 
http://www.dms.umontreal.ca/~andrew/PDF/PrimeRace.pdf
is likely to tell you all you want to know about this, and then a little more besides. It's a wellknown nice problem. http://www.math.umn.edu/~focm/c_/Martin.pdf is a slightly more sophisticated article for people with a small amount of analytic number theory background (that is, who know a Dirichlet Lfunction from a hole in the ground), amongst whom I once counted myself but now don't. Last fiddled with by fivemack on 20080204 at 22:36 
20080204, 22:41  #5  
"Lucan"
Dec 2006
England
14512_{8} Posts 
Quote:
I take it the answer wasn't "yes" then OTOH If I interpret "nice" as meaning "subtle", then I think that "yes" is good enough for my present purposes. Last fiddled with by davieddy on 20080204 at 22:56 

20080204, 23:32  #6 
"Lucan"
Dec 2006
England
14512_{8} Posts 

20080205, 02:29  #7 
May 2003
7·13·17 Posts 

20080205, 17:56  #8 
"Lucan"
Dec 2006
England
1100101001010_{2} Posts 
My "purpose" was to investigate the Wagstaff conjecture.
The probability of 2^p1 being prime involves ln(ap) where a=2 if p==3 mod 4 and a=6 if p==1 mod 4. Commonly we take ln(ap)~ln(p) , true for huge p. But for p in the GIMPS range I calculate ln(ap)~1.07 ln(p), an appreciable discrepancy. http://primes.utm.edu/mersenne/heuristic.html Last fiddled with by davieddy on 20080205 at 18:52 
20080205, 19:18  #9  
"Lucan"
Dec 2006
England
6474_{10} Posts 
Quote:
ln(2)~0.7 ln(6)~1.8 2.5 is 7% of 36. Last fiddled with by davieddy on 20080205 at 19:26 

20080206, 13:38  #10  
"Lucan"
Dec 2006
England
14512_{8} Posts 
Quote:
told me what I needed to know. David 

20080206, 23:31  #11 
∂^{2}ω=0
Sep 2002
República de California
2D32_{16} Posts 

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