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what is the sum of digits of the number 2^1000
 Dec 15, 2013
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2 1000 = 2*2*2*2*2*2... do this 1000 times then add all the digits

In base 10 this number is 302 digits long.
Numbers of this length (and longer) are usually found in RSA and DH security keys. They are usually stored in hex (0x) h form.

1+0+7+1+5+0+8+6+0+7+1+8+6+2+6+7+3+2+0+...+...+6

This is a rather tedious and error prone exercise to do by hand or with a calculator. A simple computer program converting the number to a string array then adding the elements would make it easy.

The complete number in base 10 is displayed below. I'll leave the addition (or programing) to you.

2 1000 =
1071508607186267320948425049060001810561404811705533607443750388370351051124936122493198378815695858127594672917553146825187145285692
3140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542
167660429831652624386837205668069376
 Dec 15, 2013

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