I felt that I needed to clarify another point

in the second question. So here I will post

the restated CONTEST++ in its entirety:

I offer a $51 prize to the first person who can submit

a verifiable counterexample by New Year's day

either for the following conjectures.

(x,A,B,c,k,f : integers)

Let A = 20x^2 + 10x + 1;

Let B = 10x^2 + 4x + 1;

Let c = trunc(A/sqrt(5)) - 1;

1) For any x > 0, apply the issquare test to each k

in the interval c <= k < B.

If there exists a value of k that satisfies the

conditions of the test, then A is composite,

and there will be at least one value of k such

that 2*k - 1 will have a factor in A.

(issquare test: 0 < 5*(2*k -1)^2 - 4*A^2 = f^2)

2) For any x > 0, if A and B are placed in the formula

below, the five values can be used to make a polynomial

or a set of difference equations that will generate a

fourth degree sequence.

A^2 , A^2 + 1*B*10 , A^ + 4*B*10 + 60,

A^2 + 9*B*10 + 360, A^2 + 16* B*10 + 1200

The result will always be either a pure +1 mod 10 sequence

(all prime factors end in one) or a defective +1 mod 10

sequence (all prime factors end in one, except for a

finite number of distinct squares of primes that end in

nine occurring at regular intervals):

As I really want these questions settled, I would be happy

to assist any interested person.

Aldrich