Prime Diophantine Equations

is Prime Iff the 14 Diophantine Equations in 26 variables

$\quad wz+h+j-q=0$ (1)

$\quad (gk+2g+k+1)(h+j)+h-z=0$ (2)

$\quad 16(k+1)^3(k+2)(n+1)^2+1-f^2=0$ (3)

$\quad 2n+p+q+z-q=0$ (4)

$\quad e^3(e+2)(a+1)^2+1-o^2=0$ (5)

$\quad (a^2-1)y^2+1-x^2=0$ (6)

$\quad 16r^2y^4(a^2-1)+1-u^2=0$ (7)

$\quad n+l+v-y=0$ (8)

$\quad (a^2-1)l^2+1-m^2=0$ (9)

$\quad ai+k+1-l-i=0$ (10)

$\quad \{[a+u^2(u^2-a)]^2-1\}(n+4dy)^2+1-(x+cu)^2=0$ (11)

$\quad p+l(a-n-1)+b(2an+2a-n^2-2n-2)-m=0$ (12)

$\quad q+y(a-p-1)+s(2ap+2a-p^2-2p-2)-x=0$ (13)

$\quad z+pl(a-p)+t(2ap-p^2-1)-pm=0$ (14)

have a Positive integral solution.

References

Riesel, H. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, p. 39, 1994.

$\quad wz+h+j-q=0$	(1)
$\quad (gk+2g+k+1)(h+j)+h-z=0$	(2)
$\quad 16(k+1)^3(k+2)(n+1)^2+1-f^2=0$	(3)
$\quad 2n+p+q+z-q=0$	(4)
$\quad e^3(e+2)(a+1)^2+1-o^2=0$	(5)
$\quad (a^2-1)y^2+1-x^2=0$	(6)
$\quad 16r^2y^4(a^2-1)+1-u^2=0$	(7)
$\quad n+l+v-y=0$	(8)
$\quad (a^2-1)l^2+1-m^2=0$	(9)
$\quad ai+k+1-l-i=0$	(10)
$\quad \{[a+u^2(u^2-a)]^2-1\}(n+4dy)^2+1-(x+cu)^2=0$	(11)
$\quad p+l(a-n-1)+b(2an+2a-n^2-2n-2)-m=0$	(12)
$\quad q+y(a-p-1)+s(2ap+2a-p^2-2p-2)-x=0$	(13)
$\quad z+pl(a-p)+t(2ap-p^2-1)-pm=0$	(14)