In 1976, Jones-Sata-Wada-Weins published (see here) the following polynomial $P$ of degree $25$ in $26$ variables $a$, $b$, $c$,..., $z$, admitting the property that $P(\mathbb{N})\cap \mathbb{N} = \mathbb{P}$, the set of prime numbers !

$P(a,b,...,z) = (k+2)[1 – (wz+h+j–q)^{2} – [(gk+2g+k+1)(h+j) + h – z]^{2} -(2n+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}– [16r^{2}y^{4}(a^{2}–1) + 1 – u^{2}]^{2}– [((a+u^{2}(u^{2}–a))^{2}–1)(n+4dy)^{2} + 1 – (x+cu)^{2}]^{2} –[n+l+ $ $ v–y]^{2}– [(a^{2}–1)l^{2} + 1 – m^{2}]^{2} – [ai+k+1–l–i]^{2} – [p + l(a–n–1) + b(2an+2a–n^{2}–2n–2) – m]^{2} – $ $ [q+ y(a–p–1) + s(2ap + 2a – p^{2} – 2p – 2)– x]^{2}– [z + pl(a–p) + t(2ap – p^{2} – 1) – pm]^{2}]$

Is there anything to say about prime numbers by using this polynomial and differential calculus ?