Answer
See below.
Work Step by Step
For that the expected cash prize must be greater than $1$. The expected cash prize is the sum of all the probabilities and winnings multiplied. Let $x$ be the jackpot.
$x\cdot0.00000000386+1,000,000\cdot0.00000005408+5000\cdot0.00001892689+50\cdot0.00009328256+5\cdot0.00342036036+2\cdot0.01770813839+1\cdot0.04674948535\gt1\\x\cdot0.00000000386+0.25264614193\gt1\\x\cdot0.00000000386\gt0.74735385807\\x\gt\frac{0.74735385807}{0.00000000386}\approx1.93614989137305699481865284974093264248704663212435233× 10^8$
