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Hi there, distinguished audience,

Let f(n)=n2+n+41.

further, require n to be a positive integer.
Look at the cases when f(n) is a prime number, or a composite number.
Beautiful parabola patterns appear.
see attached

writeup_for_prime_producing_trinomial_final.pdf

I also look at the case when there is

n2+n+17.

see

Lucky Number of Euler -- from Wolfram MathWorld

I can be reached by email at

matthewcharlesanderson2@gmail.com

also,

https://mattanderson.fun

Regards,

Matthew
prime

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