You could keep multiplying m by itself, sure, but in practice you're dealing with numbers so huge that it rapidly becomes impractical to test all values in the range m^2 to whatever (e.g. m^49863657239487123495780934672309687239458732946585601239587146245192587126978563425981758234729374837833000023013834769482349111943853593463798) before you finally stumble on the correct one.

Effort is better spent trying to factor the public modulus n which you already have. Because the private exponent(m^498636... above) can be derived from it.