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What is the largest known twin-prime of the form $2^acdot 3^bpm 1$?
The Next CEO of Stack OverflowDisprove the Twin Prime Conjecture for Exotic PrimesCan the twin prime conjecture be solved in this way?Is a probable prime known larger than the largest known prime?Possible method to prove infinite twin prime conjectureIs it possible a Bonse's inequality for twin primes, on assumption of a form of the Twin Prime conjecture?Smallest twin-prime-pair above $2uparrowuparrow 5 $?Twin prime pairs of the form $(prod_j=1^n phi(j))pm 1$A twin prime theorem, and a reformulation of the twin prime conjectureAn approach to proving the twin prime conjectureCan the analysis of periodic functions be applied to the twin prime conjecture?
$begingroup$
$$2^2176cdot 3^2175pm1$$ is an example of a twin-prime pair of the form $$2^acdot 3^bpm 1$$ with positive integers $a,b$. Each prime "only" has $ 1 693 $ digits, so larger examples probably exist.
Have such twin-primes be searched upto a high range ? If yes, what is the largest known twin-prime of this form ?
Update : Enzo Creti found the twin-prime $$2^5211cdot 3^5794pm1$$ with $4 334$ digits each.
number-theory elementary-number-theory reference-request prime-numbers prime-twins
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
$endgroup$
add a comment |
$begingroup$
$$2^2176cdot 3^2175pm1$$ is an example of a twin-prime pair of the form $$2^acdot 3^bpm 1$$ with positive integers $a,b$. Each prime "only" has $ 1 693 $ digits, so larger examples probably exist.
Have such twin-primes be searched upto a high range ? If yes, what is the largest known twin-prime of this form ?
Update : Enzo Creti found the twin-prime $$2^5211cdot 3^5794pm1$$ with $4 334$ digits each.
number-theory elementary-number-theory reference-request prime-numbers prime-twins
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
$endgroup$
$begingroup$
This doesn't identify any such primes, but it is of relevance in the search: If $2^a3^bpm 1$ are primes, then $|a-b|equiv 1 mod2$. If otherwise, the final digit of $2^a3^b$ will be either $4$ or $6$, making one of $2^a3^bpm 1$ divisible by $5$. The exception to that parity rule is $5$ itself in the twin prime pair $5,7$, where $a=b=1$.
$endgroup$
– Keith Backman
Jan 22 at 14:39
1
$begingroup$
Btw $2^3505cdot 3^2892 pm 1$ is a larger example.
$endgroup$
– Sil
Mar 17 at 22:40
add a comment |
$begingroup$
$$2^2176cdot 3^2175pm1$$ is an example of a twin-prime pair of the form $$2^acdot 3^bpm 1$$ with positive integers $a,b$. Each prime "only" has $ 1 693 $ digits, so larger examples probably exist.
Have such twin-primes be searched upto a high range ? If yes, what is the largest known twin-prime of this form ?
Update : Enzo Creti found the twin-prime $$2^5211cdot 3^5794pm1$$ with $4 334$ digits each.
number-theory elementary-number-theory reference-request prime-numbers prime-twins
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
$endgroup$
$$2^2176cdot 3^2175pm1$$ is an example of a twin-prime pair of the form $$2^acdot 3^bpm 1$$ with positive integers $a,b$. Each prime "only" has $ 1 693 $ digits, so larger examples probably exist.
Have such twin-primes be searched upto a high range ? If yes, what is the largest known twin-prime of this form ?
Update : Enzo Creti found the twin-prime $$2^5211cdot 3^5794pm1$$ with $4 334$ digits each.
number-theory elementary-number-theory reference-request prime-numbers prime-twins
number-theory elementary-number-theory reference-request prime-numbers prime-twins
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
edited Mar 19 at 11:00
Peter
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
asked Jan 20 at 10:36
PeterPeter
49.1k1240137
49.1k1240137
$begingroup$
This doesn't identify any such primes, but it is of relevance in the search: If $2^a3^bpm 1$ are primes, then $|a-b|equiv 1 mod2$. If otherwise, the final digit of $2^a3^b$ will be either $4$ or $6$, making one of $2^a3^bpm 1$ divisible by $5$. The exception to that parity rule is $5$ itself in the twin prime pair $5,7$, where $a=b=1$.
$endgroup$
– Keith Backman
Jan 22 at 14:39
1
$begingroup$
Btw $2^3505cdot 3^2892 pm 1$ is a larger example.
$endgroup$
– Sil
Mar 17 at 22:40
add a comment |
$begingroup$
This doesn't identify any such primes, but it is of relevance in the search: If $2^a3^bpm 1$ are primes, then $|a-b|equiv 1 mod2$. If otherwise, the final digit of $2^a3^b$ will be either $4$ or $6$, making one of $2^a3^bpm 1$ divisible by $5$. The exception to that parity rule is $5$ itself in the twin prime pair $5,7$, where $a=b=1$.
$endgroup$
– Keith Backman
Jan 22 at 14:39
1
$begingroup$
Btw $2^3505cdot 3^2892 pm 1$ is a larger example.
$endgroup$
– Sil
Mar 17 at 22:40
$begingroup$
This doesn't identify any such primes, but it is of relevance in the search: If $2^a3^bpm 1$ are primes, then $|a-b|equiv 1 mod2$. If otherwise, the final digit of $2^a3^b$ will be either $4$ or $6$, making one of $2^a3^bpm 1$ divisible by $5$. The exception to that parity rule is $5$ itself in the twin prime pair $5,7$, where $a=b=1$.
$endgroup$
– Keith Backman
Jan 22 at 14:39
$begingroup$
This doesn't identify any such primes, but it is of relevance in the search: If $2^a3^bpm 1$ are primes, then $|a-b|equiv 1 mod2$. If otherwise, the final digit of $2^a3^b$ will be either $4$ or $6$, making one of $2^a3^bpm 1$ divisible by $5$. The exception to that parity rule is $5$ itself in the twin prime pair $5,7$, where $a=b=1$.
$endgroup$
– Keith Backman
Jan 22 at 14:39
1
1
$begingroup$
Btw $2^3505cdot 3^2892 pm 1$ is a larger example.
$endgroup$
– Sil
Mar 17 at 22:40
$begingroup$
Btw $2^3505cdot 3^2892 pm 1$ is a larger example.
$endgroup$
– Sil
Mar 17 at 22:40
add a comment |
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$begingroup$
This doesn't identify any such primes, but it is of relevance in the search: If $2^a3^bpm 1$ are primes, then $|a-b|equiv 1 mod2$. If otherwise, the final digit of $2^a3^b$ will be either $4$ or $6$, making one of $2^a3^bpm 1$ divisible by $5$. The exception to that parity rule is $5$ itself in the twin prime pair $5,7$, where $a=b=1$.
$endgroup$
– Keith Backman
Jan 22 at 14:39
1
$begingroup$
Btw $2^3505cdot 3^2892 pm 1$ is a larger example.
$endgroup$
– Sil
Mar 17 at 22:40