Q$1$: a$)$ Develop an efficient algorithm to find a list of prime numbers from $100$ to $(2$ Marks$)$ b$)$ Differentiate between Polynomial$-$time and exponential$-$time algorithms. Give $(2$ Marks$)$ an example of one problem each for these two running times. c$)$ Using Horner's rule, evaluate the polynomial p$($x$)=2$x$^(5)-5$x$^(4)-3$x$^(2)+15$ at x$=2.$ Analyse the computation time required for polynomial evaluation using $(2$ Marks$)$ Horner's rule against the Brute force method. d$)$ State and explain the theorems for computing the bounds O$,\backslash$Omega and $\backslash$Theta $.$ Apply $(4$ Marks$)$ these theorem to find the O$-$notation, $\backslash$Omega$-$notation and $\backslash$Theta$-$notation for the function: f$($n$)=10$n$^(3)+18$n$^(2)+1$ e$)$ Explain binary exponentiation for computing the value $5^(19).$ Write the right$-$to$-$ left binary ex