Prime testing


True or False

9840293798402937 is a prime number?


If an odd integer n>1n>1 satisfies 2n11(modn){ 2 }^{ n-1 }\equiv 1(mod\quad n), then nn must be a prime?

What is the smallest number that doesn't satisfy the above statement?

When n=3n = 3, 2n3=52^{n}-3 = 5. This is the first value of nn for which 2n32^n - 3 is prime. What is the 2424th value of nn such that 2n32^{n}-3 is a prime number?


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