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Which number comes the next?

3,5,17,257,?

Note: The answer is the last term of the series.


The answer is 65537.

Nikhar Rakhashia by Nikhar Rakhashia , 24, India

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3 solutions

All terms are part of 2 2 n + 1 {2}^{{2}^{n}}+1

The solution, 65537, is the last on the series only if those are Fermat Primes. The formula to find these numbers gives infinite terms, being next one 4294967297, that is also a Fermat Number, altough not a Fermat Prime.

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Vaibhav Kandwal
Jan 16, 2015

I did it like this : 2 1 + 1 , 2 2 + 1 , 2 4 + 1 , 2 8 + 1 2^1+1, 2^2+1, 2^4+1, 2^8+1 , so last one would be 2 1 6 + 1 2^16+1

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A hint is provided in the question itself !!! .

These are Fermat Primes .

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