Whilst the basic architecture is somewhat more secure, for instance enforcing root user distinction, Linux is certainly not immune to viruses. But users tend to be more savy and it tends to be used less as a general purpose os and more as a specialised one thus the chance of viruses being run are less. Those reasons often makes it less profitable for virus writers to target the os.
The first worm, the Morris worm, was very succesfull against unix systems in the late 80s
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