• Feb 4th 2006, 12:23 PM
dahamalian2000
hi, I am having trouble proving or disproving these two:

First:

If p is a prime number, must 2^p - 1 also be prime? Prove or give a counterexample.

Second:

If n is a nonnegative integer, must 2^(2^n) + 1 be prime? Prove of give a couterexample.

Thank you so much.
• Feb 4th 2006, 12:29 PM
CaptainBlack
Quote:

Originally Posted by dahamalian2000
hi, I am having trouble proving or disproving these two:

First:

If p is a prime number, must 2^p - 1 also be prime? Prove or give a counterexample.

$
p=11,\ 2^p-1=2047=23 \times 89
$

RonL
• Feb 4th 2006, 12:34 PM
CaptainBlack
Quote:

Originally Posted by dahamalian2000

Second:

If n is a nonnegative integer, must 2^(2^n) + 1 be prime? Prove of give a couterexample.

$
n=5,\ 2^{2^n}+1=2^{32}+1=4294967297=641 \times 6700417
$

RonL
• Feb 4th 2006, 01:05 PM
dahamalian2000
Thanks! But do you know a way to generally disprove it, using variables?

Thank again,
David
• Feb 4th 2006, 01:32 PM
CaptainBlack
Quote:

Originally Posted by dahamalian2000
Thanks! But do you know a way to generally disprove it, using variables?

Thank again,
David

No

RonL
• Feb 4th 2006, 02:37 PM
ThePerfectHacker
Quote:

Originally Posted by dahamalian2000
Thanks! But do you know a way to generally disprove it, using variables?

Thank again,
David

NOT even Fermat himself had a way to disprove it with
variables.