Unless you want your name printed on the ballot, you do not need any signatures. Write-in votes are allowed in most , if not all states. If you want to be on the ballot,the number of signatures required varies from state to state from 5000 to something like 45,000. You have to file a separate petition in each state, and of course all signatures must be valid and verifiable. You usually would need to have at least 20% more than the required minimum. You also have to pay a fee in most states. The wikipedia link gives more details.
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If a U.S. Senator wants to run for President of the United States, he must go through the electoral procedures of any other candidate for President of the United States.
Senators are elected by direct popular vote. In order to win, you need one more vote than any of your opponents. That number varies depending on the number of voters in the state.
To be declared the winner, a candidate needs at least 270 electoral college votes.
majority on electoral votes
more than 50%
How a state allocates its electoral votes is up to that state. Most states allocate all electoral votes to the candidate with more votes than any other candidate in that state; this is called a plurality. Note, however, that some states require the electors to cast their ballots in the Electoral College for the winner of the popular vote, but others have no such requirement.
In the end Adams received 71 electoral votes, winning the election. Jefferson finished second with 68 votes. under the provisions of the Constitution at that time, the person with the second-highest number of electoral votes became vice president. Jefferson therefore became the new vice president. The administration that took office on March 4, 1797, had a Federalist president and Republican vice president. :D