# Prime number proof

prove if the statement is true, else form it's negation and prove that is true:

## \forall y \in (x | x \in \mathbb Z , x \geq 1), 5y^2 + 5y + 1 ##

I think it's true, but I can't really even get started to prove it

I really suck at these and need help please, thank you!

## Answers and Replies

mfb
Mentor
There is no statement that could be evaluated as true or false.
It is like "prove that this is true or false: 5".

I guess there is "is prime" missing. Did you test some numbers to check it? Don't just check small numbers, consider larger numbers as well.

Big hint:
There is no known useful formula to generate an arbitrary number of primes without excessive calculations.

.Scott
Homework Helper
Put this text into an *.vbs file and run it:

For y = 1 To 100
z = 5*y*y + 5*y + 1
if (z mod 11)=0 then MsgBox("f(" & y & ") is divisible by 11.")
if (z mod 19)=0 then MsgBox("f(" & y & ") is divisible by 19.")
Next

HallsofIvy
Science Advisor
Homework Helper
Where did "divisible by 5" and "divisible by 11" come from?