Historical Math Problem

[greatwhiteshark]

Pierre de Fermat (1601-1665) conjectured that the function
f(x) = 2^(2x) + 1 for x = 1, 2, 3, ..., would always have a value equal to a prime number. But Leonhard Euler (1707-1783) showed that this formula fails for x = 5. Use a calculator to determine the prime numbers produced by f for x = 1, 2, 3, 4. Then show that f(5) = 641(6,700,417), which is NOT prime.

 

[jolly]

 

[greatwhiteshark]

jolly

Please, stop answering my questions. You like to put students down with your Einstein knowledge of math. I do NOT place my questions here to be insulted. Do you know this or do you know that?
If I did Einstein, would I ask anyone here for help???????

PLEASE, skip my questions. I want patient tutors to reply. Stop answering my questions! OKAY??? Got it????

 

[tkhunny]

Well, let's see...

2^2*5 + 1 = 2¹⁰ + 1 = 1024 + 1 = 1025

1025 = 5²*41 -- Clearly NOT prime.

I'm having rouble believing Fermat wouldn't have noticed that.
I'm also wondering why 1025 has nothing to do with the reported values.

On the other hand, 2^2*16 + 1 = 42949697297 = 641*6700417

Although still a bit dubious, I suppose I can believe that may have been beyond the scope of Fermat.

Are you CERTAIN you copied the problem correctly?

 

[pka]

Janet,
While Einstein was the most important physicist of the twentieth century, he was only fair at mathematics.

Now, you have written this famous problem incorrectly.
It should be: f(x)=2^{2^x}+1.

 

[greatwhiteshark]

ok

Much better replies. Pka, thank you. Thank you all for your great help.