We solve this using special relativity. Special relativity actually places the relativistic mass to be the rest mass factored by a constant "gamma". The gamma is equal to 1/sqrt (1 - (v/c)^2).
We want a ratio of 3000000 to 1, or 3 million to 1.
Therefore:
3E6 = 1/sqrt (1 - (v/c)^2)
1 - (v/c)^2 = (0.000000333)^2
0.99999999999999 = (v/c)^2
0.99999999999999 = v/c
v= 99.999999999999% of the speed of light ~ speed of light
v = 3 x 10^8 m/s