Are my potential GRE scores up to par?

Colleges and Universities A-Z Harvard University
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Hi all. So I am currently an undergraduate history major at a small private Christian liberal arts college and was wondering if my hoped for GRE scores are competitive enough for the schools I’m applying to.So far I’ve taken several GRE practice exams and my scores are-Quantitative: 161, Verbal: 165.
I plan on applying to Harvard, Yale, and Princeton for the history of science graduate program. Also my current GPA is a 3.58, but will likely become at least a 3.6 before I graduate.

Are my credentials competitive enough for Harvard graduate school?Also my essays are very good-I’ve written an excellent statement of purpose as well as a 20 page writing sample(20 pages is the max) for this program that I am interested in.
What are your thoughts?

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^^ This is the undergraduate forum for Harvard College. Questions related to graduate school (Harvard’s & others) should be posted here: http://talk.collegeconfidential.com/graduate-school/