How many generations have past from Adam to the present according to the Torah?
The Biblical count of generations from Adam to Moshe (Moses) was 26 generations. From Moshe to the present is much more arbitrary, and I think would depend on how many years we use as an average per generation. The generations from Moshe forward are far shorter than the generations we use in counting pre-Moshe.
If we choose 25 years for an average post-Moshe generation, then it is four generations per one hundred years. 3,400 years have elapsed since the birth of Moshe and that would be 136 generations. Adding the first 26 you have a total of 162 generations. If you opt for a smaller number per generation you will arrive at a larger total, a larger number, then a smaller total.
Regards,
Eliahu Levenson