A number theory problem by mustafa rokadiya

For a natural no. 'n' : 2^{2}^{n}+1 is a prime is : [e.g.: for n=1, 2^{2}^{1} +1 = 5. which is prime no. Hence, it is true.]

true for n=1,2,3,4,5 true for n=1,2 true for n=1,2,3,4 always true

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2 solutions

Josh Speckman
Apr 15, 2014

These numbers are called Fermat Numbers , and for a long time they were thought to be automatically prime. Leonard Euler found that the 5 th 5^{\text{th}} Fermat Number, 4294967297 4294967297 , was not in fact prime. being divisible by 641 641 . Thus the conjecture that all numbers of this form are prime is false, and it is only valid for n = 0 , 1 , 2 , 3 , 4 n={0,1,2,3,4}

Chinmay Patil
Mar 30, 2014

2^2^5 +1= not a prime number

how can you say it is not a prime number. it is 4294967297

Kushagra Sahni - 7 years, 2 months ago

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Try to divide it by basic odd numbers. It's a prime number

Chinmay Patil - 7 years, 2 months ago

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