Let $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right],{\mathrm{a}}_{\mathrm{ij}}\in \mathrm{Z}\cap [0,4],1\le \mathrm{i},\mathrm{j}\le 2$. The number of matrices A such that the sum of all entries is a prime number $\mathrm{p}\in (2,13)$ is _____.

p can be 3,5,7,11
$\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=3,\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\in \{0,1,2,3,4\}$
coefficient of ${\mathrm{x}}^3\text{ in }{\left(1+\mathrm{x}+{\mathrm{x}}^2+{\mathrm{x}}^3+{\mathrm{x}}^4\right)}^4={\left(1-{\mathrm{x}}^5\right)}^4(1-\mathrm{x}{)}^{-4}$
$\begin{array}{l}=\left(1{-}^4{\mathrm{C}}_1{\mathrm{x}}^5{+}^4{\mathrm{C}}_2{\mathrm{x}}^{10}-\dots \right)\left(1{+}^4{\mathrm{C}}_1{+}^5{\mathrm{C}}_2{\mathrm{x}}^2{+}^6{\mathrm{C}}_3{\mathrm{x}}^3{+}^7{\mathrm{C}}_4{\mathrm{x}}^4+----\right)\\ {=}^6{\mathrm{C}}_3=20\end{array}$
If $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=5\to \text{ coefficient of }{\mathrm{x}}^5\text{ in }{\left(1+\mathrm{x}+---+{\mathrm{x}}^4\right)}^4{=}^8{\mathrm{C}}_5-4.1=52$
If $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=7\to \text{ coefficient of }{\mathrm{x}}^7\text{ in }{\left(1+\mathrm{x}+---+{\mathrm{x}}^4\right)}^4{=}^{10}{\mathrm{C}}_7{-}^{4.5}{\mathrm{C}}_2=120-40$
$\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=11\to$coefficient of x¹¹ in 
${\left(1+\mathrm{x}+{\mathrm{x}}^2+---+{\mathrm{x}}^4\right)}^4{=}^{14}{\mathrm{C}}_{11}{-}^{4.9}{\mathrm{C}}_6{+}^4{\mathrm{C}}_2{\cdot }^4{\mathrm{C}}_1=364-336+24$
Total matrices $=20+52+80+52=204$