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/** From:
Diophantine Representation of the Set of Prime Numbers
James P. Jones, Daihachiro Sato, Hideo Wada, and Douglas Wiens
"The set of prime numbers is identical with the set of positive values taken
on by the polynomial" (below) "as the variables range over the nonnegative
integers."
https://math.umd.edu/~laskow/Pubs/713/Diorepofprimes.pdf
*/
prime[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z] :=
{
(k+2)*(1-(w z + h + j - q)^2 - ((g k + 2 g + k + 1)*(h + j) + h - z)^2 -
(2 n + p + q + z - e)^2 - (16 (k+1)^3 * (k + 2) * (n+1)^2 + 1 - f^2)^2 -
(e^3 * (e+2)(a+1)^2 + 1 - o^2)^2 - ((a^2-1) y^2 + 1 - x^2)^2 -
(16 r^2 y^4 (a^2 - 1) + 1 - u^2)^2 -
(((a + u^2 (u^2 - a))^2 - 1) * (n + 4 d y)^2 + 1 - (x + c u)^2)^2 -
(n + l + v - y)^2 - ((a^2 - 1) l^2 + 1 - m^2)^2 -
(a i + k + 1 - l - i)^2 -
(p + l(a - n - 1) + b (2 a n + 2 a - n^2 - 2 n - 2) - m)^2 -
(q + y (a - p - 1) + s (2 a p + 2 a - p^2 - 2 p - 2) - x)^2 -
(z + p l (a - p) + t (2 a p - p^2 - 1) - p m)^2)
}
/** Version of the function that takes an array of 26 values. */
prime[array] :=
{
[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z] = array
prime[a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z]
}
Download or view diophantinePrimes.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen, eliasen@mindspring.com