How many primes of the form $2^p-p$ with $p$ prime?
$begingroup$
I know that if $p = 6k+1$ with $k$ integer, then $(2^p-p) mod 6 equiv 1$. I think that this means that $2^p-p$ could be prime. My question is: are there a finite or infinite number of primes which can be written like this?
number-theory prime-numbers
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
$endgroup$
add a comment |
$begingroup$
I know that if $p = 6k+1$ with $k$ integer, then $(2^p-p) mod 6 equiv 1$. I think that this means that $2^p-p$ could be prime. My question is: are there a finite or infinite number of primes which can be written like this?
number-theory prime-numbers
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
$endgroup$
$begingroup$
Note: All primes after 3 can be written in the form of $6k+1$ and $6k-1$
$endgroup$
– user371530
Oct 23 '16 at 1:27
$begingroup$
Also worth noting that non-prime may work: $2^9-9=503$ is prime
$endgroup$
– Joffan
Oct 23 '16 at 1:51
2
$begingroup$
oeis.org/A048744 gives the first $23$ values of $n$ for which $2^n-n$ is prime, including the prime values $n=2,3,13,19$, and $481801$.
$endgroup$
– Barry Cipra
Nov 22 '16 at 23:05
add a comment |
$begingroup$
I know that if $p = 6k+1$ with $k$ integer, then $(2^p-p) mod 6 equiv 1$. I think that this means that $2^p-p$ could be prime. My question is: are there a finite or infinite number of primes which can be written like this?
number-theory prime-numbers
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
$endgroup$
I know that if $p = 6k+1$ with $k$ integer, then $(2^p-p) mod 6 equiv 1$. I think that this means that $2^p-p$ could be prime. My question is: are there a finite or infinite number of primes which can be written like this?
number-theory prime-numbers
number-theory prime-numbers
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
edited Jun 18 '17 at 15:54
jvdhooft
5,57561641
5,57561641
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
asked Oct 23 '16 at 1:21
O. ArcilaO. Arcila
757
757
$begingroup$
Note: All primes after 3 can be written in the form of $6k+1$ and $6k-1$
$endgroup$
– user371530
Oct 23 '16 at 1:27
$begingroup$
Also worth noting that non-prime may work: $2^9-9=503$ is prime
$endgroup$
– Joffan
Oct 23 '16 at 1:51
2
$begingroup$
oeis.org/A048744 gives the first $23$ values of $n$ for which $2^n-n$ is prime, including the prime values $n=2,3,13,19$, and $481801$.
$endgroup$
– Barry Cipra
Nov 22 '16 at 23:05
add a comment |
$begingroup$
Note: All primes after 3 can be written in the form of $6k+1$ and $6k-1$
$endgroup$
– user371530
Oct 23 '16 at 1:27
$begingroup$
Also worth noting that non-prime may work: $2^9-9=503$ is prime
$endgroup$
– Joffan
Oct 23 '16 at 1:51
2
$begingroup$
oeis.org/A048744 gives the first $23$ values of $n$ for which $2^n-n$ is prime, including the prime values $n=2,3,13,19$, and $481801$.
$endgroup$
– Barry Cipra
Nov 22 '16 at 23:05
$begingroup$
Note: All primes after 3 can be written in the form of $6k+1$ and $6k-1$
$endgroup$
– user371530
Oct 23 '16 at 1:27
$begingroup$
Note: All primes after 3 can be written in the form of $6k+1$ and $6k-1$
$endgroup$
– user371530
Oct 23 '16 at 1:27
$begingroup$
Also worth noting that non-prime may work: $2^9-9=503$ is prime
$endgroup$
– Joffan
Oct 23 '16 at 1:51
$begingroup$
Also worth noting that non-prime may work: $2^9-9=503$ is prime
$endgroup$
– Joffan
Oct 23 '16 at 1:51
2
2
$begingroup$
oeis.org/A048744 gives the first $23$ values of $n$ for which $2^n-n$ is prime, including the prime values $n=2,3,13,19$, and $481801$.
$endgroup$
– Barry Cipra
Nov 22 '16 at 23:05
$begingroup$
oeis.org/A048744 gives the first $23$ values of $n$ for which $2^n-n$ is prime, including the prime values $n=2,3,13,19$, and $481801$.
$endgroup$
– Barry Cipra
Nov 22 '16 at 23:05
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
At this moment I do not have complete explanation of your question but with the use of my own properties of primes which I discovered last year I made a conclusion i.e.:
If (2p - 5) and (2p + 5) are primes than (2p - a) and (2p + a) are also primes only and only if "a" is a multiple of 5(which is rare but can come) or "a" is a prime number maybe "p" also.
7 also show similar property in (2p - 7) and (2p + 7)
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
At this moment I do not have complete explanation of your question but with the use of my own properties of primes which I discovered last year I made a conclusion i.e.:
If (2p - 5) and (2p + 5) are primes than (2p - a) and (2p + a) are also primes only and only if "a" is a multiple of 5(which is rare but can come) or "a" is a prime number maybe "p" also.
7 also show similar property in (2p - 7) and (2p + 7)
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
$endgroup$
add a comment |
$begingroup$
At this moment I do not have complete explanation of your question but with the use of my own properties of primes which I discovered last year I made a conclusion i.e.:
If (2p - 5) and (2p + 5) are primes than (2p - a) and (2p + a) are also primes only and only if "a" is a multiple of 5(which is rare but can come) or "a" is a prime number maybe "p" also.
7 also show similar property in (2p - 7) and (2p + 7)
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
$endgroup$
add a comment |
$begingroup$
At this moment I do not have complete explanation of your question but with the use of my own properties of primes which I discovered last year I made a conclusion i.e.:
If (2p - 5) and (2p + 5) are primes than (2p - a) and (2p + a) are also primes only and only if "a" is a multiple of 5(which is rare but can come) or "a" is a prime number maybe "p" also.
7 also show similar property in (2p - 7) and (2p + 7)
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
$endgroup$
At this moment I do not have complete explanation of your question but with the use of my own properties of primes which I discovered last year I made a conclusion i.e.:
If (2p - 5) and (2p + 5) are primes than (2p - a) and (2p + a) are also primes only and only if "a" is a multiple of 5(which is rare but can come) or "a" is a prime number maybe "p" also.
7 also show similar property in (2p - 7) and (2p + 7)
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
answered Dec 18 '18 at 21:03
DynamoDynamo
104517
104517
add a comment |
add a comment |
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$begingroup$
Note: All primes after 3 can be written in the form of $6k+1$ and $6k-1$
$endgroup$
– user371530
Oct 23 '16 at 1:27
$begingroup$
Also worth noting that non-prime may work: $2^9-9=503$ is prime
$endgroup$
– Joffan
Oct 23 '16 at 1:51
2
$begingroup$
oeis.org/A048744 gives the first $23$ values of $n$ for which $2^n-n$ is prime, including the prime values $n=2,3,13,19$, and $481801$.
$endgroup$
– Barry Cipra
Nov 22 '16 at 23:05