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1,024 because all the numbers between 1 and 1000 that have 2 as their only prime factor are 2,4,8,16,32,64,128,265,512 The patern is that 2 times 2 =4, 4 times 2=8, 8 times 2=16 ect. and 512 times 2 = 1,024

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Q: What is the next number after 1000 that has 2 as its only prime factor?
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