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Old 2020-07-08, 14:46   #1
drmurat
 
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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
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Old 2020-07-08, 15:24   #2
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Quote:
Originally Posted by drmurat View Post
is it possible ( 2 ^ n ) +1 and ( 2 ) ^ ( n + 1 ) + 1 can be prime
Yes, for n = 1.
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Old 2020-07-08, 15:25   #3
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Yes, for n = 1.
lol
and one more sample ?
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Old 2020-07-08, 15:42   #4
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Originally Posted by drmurat View Post
lol
and one more sample ?
n=0.
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Old 2020-07-08, 15:53   #5
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Originally Posted by paulunderwood View Post
n=0.
yes but lets try n> 1
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Old 2020-07-08, 16:04   #6
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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
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Old 2020-07-08, 16:25   #7
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Originally Posted by drmurat View Post
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.
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Old 2020-07-08, 16:29   #8
drmurat
 
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Originally Posted by sweety439 View Post
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
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Old 2020-07-08, 18:59   #9
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yes it is impossible . one of rhem is diveded by 3 all the time
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Old 2020-07-08, 19:21   #10
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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
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Old 2020-07-08, 19:34   #11
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Quote:
Originally Posted by carpetpool View Post
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
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