mersenneforum.org prime producing polynomial
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2021-06-15, 09:08   #1
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

32116 Posts
prime producing polynomial

See this polynomial

f(n) = n^2 + n + 41

assume n is a positive integer

I once received a standing ovation for a presentation on this topic at a 3 day math conference. It was at Salishan Oregon USA, at a conference for community college math teachers. I have done some community college math teaching. I hope you find this interesting.

Regards,
Matt
Attached Files
 A prime producing polynomial March 9 2021.pdf (269.4 KB, 34 views) A prime producing quadratic expression 2019 (3).pdf (473.3 KB, 16 views)

Last fiddled with by MattcAnderson on 2021-06-26 at 09:19 Reason: added slideshow file, changed trinomial name from q to f.

2021-06-16, 07:42   #2
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

32×89 Posts

Here is a list of many algebraic factorization s to find cases when
f(n) = n^2 + n + 41 is a composite number.

I used a data table from a Maple calculation to list numbers when f(n) is a composite number. Then I used the method of 3 point quadratic curve fit to list parabolas. The parabolas are parametric and for all integers on these parabolic curves, f(n) is a composite number. (There are no graphs in this file.)

look

Matt
Attached Files
 small equation coefficient doublecheck 33.pdf (631.8 KB, 13 views)

Last fiddled with by MattcAnderson on 2021-06-16 at 13:35 Reason: explained method

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