Question

Mersenne primes. So is this true or false, that if n is prime then (2^n -1) must also be prime?

Answer 1

hmmm I don't think so (could be wrong)
maybe we can try to find a counterexample

Answer 2

n=2 we have M=3
n=3 we have M=7
n=5 we have M=31
n=7 we have M=127
so far these M's have been prime
try the next prime number n

Answer 3

do you think 2^(11) -1 is prime or not?

Answer 4

yes, maybe...............

Answer 5

11 is prime

Answer 6

2047 does not divide 2,3,5,7,11,13,17, or 19.

Answer 7

2047 is composite

Answer 8

and I think you mean the other way around

Answer 9

but yeah 23 and 89 both divide 2047

Answer 10

n = 13; 8191 is prime
n = 17; 131071 is prime
n = 19; 524287 is prime
Something is wrong........... 2^11-1 should be prime.........

Answer 11

why is something wrong?

Answer 12

you found a counterexample
which means the statement above is false

Answer 13

n being prime doesn't imply M_n is prime

Answer 14

is 8388607 = 2^23-1 prime

Answer 15

That is way bigger than 2047 lol
I would have to use a computer tell me

Answer 16

i divide by numbers 1-30 none of them work. if this number is composite then i believe this statement is false

Answer 17

we already found a counterexample so you should already believe the statement is false

Answer 18

is 11 not prime?
is 2^(11)-1 not 2047 which is the product of 23 and 89?

Answer 19

ok, I am just wondering now if that is the only correction to this statement......

Answer 20

nope

Answer 21

there are probably infinitely more

Answer 22

http://en.wikipedia.org/wiki/Mersenne_prime

Answer 23

they give more counterexamples there

Answer 24

i got the link

Answer 25

like notice in there n list
they skip
11,23,29,...

Answer 26

37,41, and so on

Answer 27

http://www.wolframalpha.com/input/?i=factors+of+%282%5E%2823%29-1%29
for your question earlier

Answer 28

as you can see for n=23 M was composite
since 2^(23)-1
=47(178481)

Answer 29

no wonder you didn't find the divisors
they were pretty big

Answer 30

ok, biggest prime ever is 47983739879261

Answer 31

there should be bigger primes than that right?

Answer 32

2^.....................-1

Answer 33

(893041296^28.e+1380219695) + (3820981901^697910283685247e+3789281 +43) + 3810947265444810394765539821317422670881596

Answer 34

is prime