About k ^ 2 + 1 primes

[science_man_88]

Originally Posted by Dr Sardonicus

As written? That after-the-fact edit is the most inane attempt to whitewash a mistake I've seen in a long, long time - perhaps ever - on this Forum since I've been following it.

In the first place, how a number is written doesn't affect whether it's a Sierpinski number, or a GFN. The number 25*2^13719266 + 1 clearly is (5*2^6859633)^2 + 1, thus a GFN.

In the second place, k is a Sierpinski number when k*2^n + 1 is composite for every positive integer n. How do you claim to know that k = 25*2^13719266 + 1 has this property?

I'm guessing you don't know any such thing.

In trying to whitewash one mistake, you've made another.

Look I've been suicidal in the last few years.

[Andrew Usher]

OK, he meant Proth number/prime, not Sierpinski - I can see how one might get the terms confused, since the minus-side counterparts of both are called 'Riesel'. But for historical reasons, we have a difference.

Now the more important question is how we are to pronounce 'Proth' ...

[bur]

Like any respectable german would: pros numbe.

[Batalov]

Originally Posted by bur

Like any respectable German would: pros numbe.

Or, as allegedly, Ron DeSantis says: "Thigh food" (meaning "Thai food").

[bhelmes]

Originally Posted by DF476

I have created a little program to find the prime numbers of k ^ 2 + 1, where k is an even number (except 1). And I have been surprised by how little information there is about them. I have only found one entry in the OEIS that barely reaches 40 numbers. So I ask, is there a search project for these primes? Or do they have a name (I have thought of calling them Asfolk)? Do they have a pattern?

Thanks for reading me

You can try to improve it: http://devalco.de/quadr_Sieb_x%5E2+1.php