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 2020-07-08, 14:46 #1 drmurat   "murat" May 2020 turkey 22×19 Posts is it possible is it possible ( 2 ^ n ) +1 and ( 2 ) ^ ( n + 1 ) + 1 can be prime Last fiddled with by drmurat on 2020-07-08 at 14:46
2020-07-08, 15:24   #2
rogue

"Mark"
Apr 2003
Between here and the

11×563 Posts

Quote:
 Originally Posted by drmurat is it possible ( 2 ^ n ) +1 and ( 2 ) ^ ( n + 1 ) + 1 can be prime
Yes, for n = 1.

2020-07-08, 15:25   #3
drmurat

"murat"
May 2020
turkey

22·19 Posts

Quote:
 Originally Posted by rogue Yes, for n = 1.
lol
and one more sample ?

2020-07-08, 15:42   #4
paulunderwood

Sep 2002
Database er0rr

5×7×101 Posts

Quote:
 Originally Posted by drmurat lol and one more sample ?
n=0.

2020-07-08, 15:53   #5
drmurat

"murat"
May 2020
turkey

22×19 Posts

Quote:
 Originally Posted by paulunderwood n=0.
yes but lets try n> 1

 2020-07-08, 16:04 #6 paulunderwood     Sep 2002 Database er0rr DCF16 Posts For n > 1, N = 2^n +1 has to be a generalized Fermat prime with b=2 i.e 2^(2^a)+1, but 2^a+1 can never be a power of 2 Last fiddled with by paulunderwood on 2020-07-08 at 16:08
2020-07-08, 16:25   #7
sweety439

Nov 2016

22·691 Posts

Quote:
 Originally Posted by drmurat is it possible ( 2 ^ n ) +1 and ( 2 ) ^ ( n + 1 ) + 1 can be prime
k*2^n+1 and k*2^(n+1)+1 can be both prime only for k divisible by 3, or one of these two numbers will be divisible by 3.

2020-07-08, 16:29   #8
drmurat

"murat"
May 2020
turkey

22×19 Posts

Quote:
 Originally Posted by sweety439 k*2^n+1 and k*2^(n+1)+1 can be both prime only for k divisible by 3, or one of these two numbers will be divisible by 3.
can you give sample

 2020-07-08, 18:59 #9 drmurat   "murat" May 2020 turkey 22·19 Posts yes it is impossible . one of rhem is diveded by 3 all the time
2020-07-08, 19:21   #10
carpetpool

"Sam"
Nov 2016

2·163 Posts

Cunningham Chain of the second kind

Quote:
 Originally Posted by PrimePages A Cunningham chain of length k (of the first kind) is sequence of k primes, each which is twice the preceding one plus one. For example, {2, 5, 11, 23, 47} and {89, 179, 359, 719, 1439, 2879}. A Cunningham chain of length k (of the second kind) is a sequence of k primes, each which is twice the preceding one minus one. (For example, {2, 3, 5} and {1531, 3061, 6121, 12241, 24481}.) .
OP is mentioning a special case of this (k=2, Fermat Primes), there are only finitely such primes as Paul mentioned.

Last fiddled with by carpetpool on 2020-07-08 at 19:22

2020-07-08, 19:34   #11
drmurat

"murat"
May 2020
turkey

1148 Posts

Quote:
 Originally Posted by carpetpool Cunningham Chain of the second kind OP is mentioning a special case of this (k=2, Fermat Primes), there are only finitely such primes as Paul mentioned.
I asked it because if 2^(n) + 1 is prime and 2^(n+1) + 1 can be prime . it means
(2^n) * (2^ (2n) + 1) *(2^ (2n+1) + 1)
gives perfect number
but it is impossible . one of them is devided by 3