/** 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]
}