Number Theory Challenge for funsies:

Does there exist an infinite sequence $p_0,p_1,p_2,...$ of prime numbers such that $$p_k\in\{4p_{k-1}-1,\,4p_{k-1}+1\}\qquad (p_k=4p_{k-1}\pm1)$$for all $k\in\mathbb{Z}^+$?

Question

Number Theory Challenge for funsies:

Does there exist an infinite sequence $p_0,p_1,p_2,...$ of prime numbers such that $$p_k\in\{4p_{k-1}-1,\,4p_{k-1}+1\}\qquad (p_k=4p_{k-1}\pm1)$$for all $k\in\mathbb{Z}^+$?

anonymous · Answer

this isn't funsies this is deathsies.

tester97 · Answer

math for funsies? umm no thanks i will pass

bibby · Answer

Can there be a negative/non integer prime? IDG why Z+

anonymous · Answer

No is my final answer, btdubs

kinggeorge · Answer

I specify $\mathbb{Z}^+$ since we want $k$ to be a positive integer. It does not effect the values of the (potentially) prime numbers. Although you should assume that any prime numbers in question will be positive (even though it doesn't actually effect the result).

kinggeorge · Answer

Minor edit in case the notation was a bit confusing.

anonymous · Answer

we already know the are infinetly many primes of the form $$4n+1,4n+3$$
is this information taken to be obviuos in this problem

kinggeorge · Answer

I think those facts can be assumed if you want.

anonymous · Answer

Absolutely.

anonymous · Answer

http://math.stackexchange.com/questions/622690/does-there-exist-an-infinite-sequence-p-0-p-1-p-2-of-prime-numbers-such-tha?noredirect=1#comment1312077_622690 i had to do this

kinggeorge · Answer

While that solution is correct, I feel like it took some of the fun away :(

anonymous · Answer

lol i am sorry for taking the fun,but i found it more fun to read those views from Stack,after i posted that problem with partial solution