They, and a bare-chested man in a dhoti, were among the six who filed their papers on the first day of nominations for the July 17 election to the President's post.
Their papers, however, were liable to be rejected as none had the signatures of 50 proposers and as many seconders from the list of electors, essential for a valid nomination.
Elected members of the Lok Sabha and the Rajya Sabha and of state legislative assemblies are the electors.
The Patels told the returning officer that it would be "good" if one of them became the country's President, and the other, the Vice President, sources present there said.
All six had attached certified copies of their election cards to prove they were voters, and four had put in the Rs 15,000 as the security amount that nominees need to deposit.
On his nomination papers, filed in two sets, Vijayprakash, who, an eyewitness said, looked like a 'sadhu', wrote: "I know my nomination paper will be rejected. A layman like me cannot obtain 100 signatures. I am crazy but one should be crazy. Sir, our institutions like Parliament (are) locked and the prison of political parties.