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Welcome to my prime producing polynomial webpage.  Now a polynomial is a mathematical expression that involves both letters and numbers.  For example x2 + 1 is a polynomial.  This project focuses on the polynomial x2 + x + 41, for positive integer values x only.  I say that the mathematical word conjecture means "probably true".  There is a difference between a conjecture and a theorem.

Much of this project is "observational" and would not have been possible without the use of a computer tool.

The prime number theorem states that there are infinitely many prime numbers.  And the distribution of prime numbers goes like 1/Ln(n) where n is the n th prime number.    However this theorem does not tell you exactly what the n th prime number is.   It has been said that, “individually, the prime numbers grow like weeds, but as a group, they March with military precision.”

Currently, it is unknown if there are infinitely many primes of the form a^2+1.  Where ‘a’ is any integer.    For example.  4^2+1 is 17 a prime, but 8^2+1 is 65= 5*13, not a prime.   

Also, it is unknown to mankind if there are infinitely primes of the form h(x)=x^2+x+41.  This h(x) is called Euler’s Lucky Polynomial.    In this project, there is a graph of data points where h(y) mod x is congruent to zero.    This graph seems to have regular structure and I have been able to exactly fit parabolas to the data, as far out as I have looked.   ( divisors up to 1000).   We find this very interesting.  

Matt C. Anderson
June 26, 2017
matt.c1.anderson at gmail dot com

edit - The term bifurcation graph is incorrect.  Use the name "graph of discrete divisors".  Also, all the points in the graph are in the set of curves p(r,c).  The minimum of the curves p(r,c) with respect to x is 163*r^2/4.

November 2020
“At most two solutions conjecture”
Let h(x) = x^2 + x + 41. Let p be a prime number.   Then h(x) mod p is congruent to 0 has at most 2 solutions for a given p.  End conjecture.  

Good Stuff

My email address is matt.c1.anderson@gmail.com
I also do Facebook - search “Matt Anderson Keizer OR”
My current Facebook photo shows me holding a fish. 

This project is a collaboration.

See my other project Enumeration of k-tuples.

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Matt Anderson,
Sep 20, 2019, 7:48 PM
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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Matt Anderson,
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