A number theory problem by mustafa rokadiya
Number Theory
Level
4
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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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 Fermat Number, 4 2 9 4 9 6 7 2 9 7 , was not in fact prime. being divisible by 6 4 1 . 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