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?

See [URL]http://en.wikipedia.org/wiki/Category:Classes_of_prime_numbers[/URL]
and then google some more.

I resisted temptation to hyperlink the word google and/or add the Bart Simpson picture.

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.

Thank you Batalov
 

I found several sites listing classes of primes.

None listed additional classes using the function a*n +d.

[QUOTE=Unregistered;141004]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?[/QUOTE]

Primes of the form 4n+3 are not the Gaussian primes.

[quote=Unregistered;141004]4n+3 interger Gaussian primes[/quote]Expanding on Dr. Silverman's answer:

Gaussian primes are among the Gaussian integers. ([URL]http://en.wikipedia.org/wiki/Gaussian_prime[/URL]) Gaussian integers are complex numbers [I]a[/I]+[I]b[/I]i. Gaussian primes have either:

A) [I]a[/I] and [I]b[/I] nonzero, and [I]a[sup]2[/sup] + b[sup]2[/sup][/I] is prime,

or

B) [I]a[/I] is a prime of the form 4n+3 and [I]b[/I] = 0,

or

C) [I]a[/I] = 0 and [I]b[/I] 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 [I]Gaussian[/I] really should imply knowledge of their complex nature and that not all Gaussian primes are real integer primes.

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.