If you want a great circle (a true straight line can't exist on the surface of a sphere), you can swim or sail just a hair short of 20,000 miles and thus more than four fifths around the planet: You can enter water in Pakistan and aim for the stretch of water between Madagaskar and Africa. This way, you'll avoid the Antarctic as well and continue north unchecked and even proceeding south a bit again until you finally hit the northeastern coast of Russia. 19,940 miles to be exact, or 32,083 kilometers.
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