20080905, 19:59  #1 
3×3,299 Posts 
Primes in residual classes
Primes of form a*n+d for fixed a and d. Also known as primes congruent to d modulo a.
Special cases: 2n+1 odd primes 4n+1 Pythagorean primes 4n+3 interger Gaussian primes Any other special cases of this type that have been named? 
20080906, 03:43  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,333 Posts 
See http://en.wikipedia.org/wiki/Categor..._prime_numbers
and then google some more. I resisted temptation to hyperlink the word google and/or add the Bart Simpson picture. 
20080907, 15:45  #3 
2,341 Posts 
Thank you Batalov
I have found several sites with classes of prime numbers. However I have not found any additional classes for the function a*n+d.

20080907, 16:43  #4 
7,393 Posts 
Thank you Batalov
I found several sites listing classes of primes.
None listed additional classes using the function a*n +d. 
20080908, 00:32  #5 
Nov 2003
2^{2}×5×373 Posts 
Primes of the form 4n+3 are not the Gaussian primes.

20080909, 06:26  #6 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Expanding on Dr. Silverman's answer:
Gaussian primes are among the Gaussian integers. (http://en.wikipedia.org/wiki/Gaussian_prime) Gaussian integers are complex numbers a+bi. Gaussian primes have either: A) a and b nonzero, and a^{2} + b^{2} is prime, or B) a is a prime of the form 4n+3 and b = 0, or C) a = 0 and b is a prime of the form 4n+3. So, case B) Gaussian primes have values equal to real (i.e., imaginary part = 0) integer primes, and some folks may (sloppily) write as though those were the only Gaussian primes. However, use of the adjective Gaussian really should imply knowledge of their complex nature and that not all Gaussian primes are real integer primes. Last fiddled with by cheesehead on 20080909 at 06:28 
20080911, 12:57  #7 
3·7·11·29 Posts 
Gaussian interger primes
Perhaps I misunderstand the term interger. I thought that that indicating these were integers implied that the imaginary part must be zero.

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