The Trump phenomenon is argued to depart from current populist rise in Europe. According to a model of opinion dynamics from sociophysics the machinery of Trump's amazing success obeys well-defined counter-intuitive rules. Therefore, his success was in principle predictable from the start. The model uses local majority rule arguments and obeys a threshold dynamics. The associated tipping points are found to depend on the leading collective beliefs, cognitive biases and prejudices of the social group which undertakes the public debate. And here comes the sesame of the Trump campaign, which develops along two successive steps. During a first moment, Trump's statement produces a majority of voters against him. But at the same time, according to the model the shocking character of the statement modifies the prejudice balance. In case the prejudice is present even being frozen among voters, the tipping point is lowered at Trump's benefit. Nevertheless, although the tipping point has been lowered by the activation of frozen prejudices it is instrumental to preserve enough support from openly prejudiced people to be above the threshold. Then, as infuriated voters launch intense debate, occurrence of ties will drive progressively hostile people to shift their voting intention without needing to endorse the statement which has infuriated them. The on going debate does drive towards a majority for Trump. The possible Trump victory at November Presidential election is discussed. In particular, the model shows that to eventually win the Presidential election, Trump must not modify his past shocking attitude but to appeal to a different spectrum of frozen prejudices, which are common to both Democrats and Republicans.