GCC and C program use help

I am very very very new at this, just taking my first class in C programming in UNIX.  Anyway, I am trying to use Cygwin, on my local machine since I will be away from internet access and will not be able to connect to my universities UNIX system.

I am having trouble getting my programs to run, I am testing and program I know compiles and runs correctly.
This is what my command screen looks like

User@ComputerName ~/Cygwin
$ gcc -o project1 project1.c

it compiles correctly, then I try what normally works on my normal UNIX system
$ project1
and I get an error
bash: project1:command not found.

Any help would be greatly appreciated, I appoligize for this greenhorn question.

thanks