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Primality test calulating on paper. Specific case
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up vote
0
down vote
favorite
How to make primality test on paper without any calculator for high numbers like
$$
(32^200) - 1
$$
$$
(400^555) - 1
$$
What specific test is useful in such cases: $$(a^b) - 1$$ where a and b are high numbers), Fermat's theorem, AKS or is there any other test that shows that this equation is prime number?
cryptography primality-test
asked Jul 16 at 17:36
Some1
63
add a comment |Â
up vote
0
down vote
favorite
How to make primality test on paper without any calculator for high numbers like
$$
(32^200) - 1
$$
$$
(400^555) - 1
$$
What specific test is useful in such cases: $$(a^b) - 1$$ where a and b are high numbers), Fermat's theorem, AKS or is there any other test that shows that this equation is prime number?
cryptography primality-test
asked Jul 16 at 17:36
Some1
63
As long as $a>2$ or $b$ is composite, one can just write down a factor of $a^b-1$.
– Lord Shark the Unknown
Jul 16 at 17:44
...but even if $a>2$ and $b$ is prime, $a^b - 1$ can be composite.
– David G. Stork
Jul 16 at 18:55
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How to make primality test on paper without any calculator for high numbers like
$$
(32^200) - 1
$$
$$
(400^555) - 1
$$
What specific test is useful in such cases: $$(a^b) - 1$$ where a and b are high numbers), Fermat's theorem, AKS or is there any other test that shows that this equation is prime number?
cryptography primality-test
asked Jul 16 at 17:36
Some1
63
How to make primality test on paper without any calculator for high numbers like
$$
(32^200) - 1
$$
$$
(400^555) - 1
$$
What specific test is useful in such cases: $$(a^b) - 1$$ where a and b are high numbers), Fermat's theorem, AKS or is there any other test that shows that this equation is prime number?
cryptography primality-test
asked Jul 16 at 17:36
Some1
63
edited Jul 16 at 17:51
asked Jul 16 at 17:36
Some1
63
asked Jul 16 at 17:36
Some1
63
asked Jul 16 at 17:36
Some1
63
63
As long as $a>2$ or $b$ is composite, one can just write down a factor of $a^b-1$.
– Lord Shark the Unknown
Jul 16 at 17:44
...but even if $a>2$ and $b$ is prime, $a^b - 1$ can be composite.
– David G. Stork
Jul 16 at 18:55
add a comment |Â
As long as $a>2$ or $b$ is composite, one can just write down a factor of $a^b-1$.
– Lord Shark the Unknown
Jul 16 at 17:44
...but even if $a>2$ and $b$ is prime, $a^b - 1$ can be composite.
– David G. Stork
Jul 16 at 18:55
As long as $a>2$ or $b$ is composite, one can just write down a factor of $a^b-1$.
– Lord Shark the Unknown
Jul 16 at 17:44
As long as $a>2$ or $b$ is composite, one can just write down a factor of $a^b-1$.
– Lord Shark the Unknown
Jul 16 at 17:44
...but even if $a>2$ and $b$ is prime, $a^b - 1$ can be composite.
– David G. Stork
Jul 16 at 18:55
...but even if $a>2$ and $b$ is prime, $a^b - 1$ can be composite.
– David G. Stork
Jul 16 at 18:55
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
$a-1$ is a factor of $a^b-1$. So if $a>2$, then $a^b-1$ is composite. For the case of $a=2$, you are looking for Mersenne primes.
answered Jul 16 at 17:42
paw88789
28.2k12248
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
$a-1$ is a factor of $a^b-1$. So if $a>2$, then $a^b-1$ is composite. For the case of $a=2$, you are looking for Mersenne primes.
answered Jul 16 at 17:42
paw88789
28.2k12248
add a comment |Â
up vote
3
down vote
accepted
$a-1$ is a factor of $a^b-1$. So if $a>2$, then $a^b-1$ is composite. For the case of $a=2$, you are looking for Mersenne primes.
answered Jul 16 at 17:42
paw88789
28.2k12248
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
$a-1$ is a factor of $a^b-1$. So if $a>2$, then $a^b-1$ is composite. For the case of $a=2$, you are looking for Mersenne primes.
answered Jul 16 at 17:42
paw88789
28.2k12248
$a-1$ is a factor of $a^b-1$. So if $a>2$, then $a^b-1$ is composite. For the case of $a=2$, you are looking for Mersenne primes.
answered Jul 16 at 17:42
paw88789
28.2k12248
answered Jul 16 at 17:42
paw88789
28.2k12248
answered Jul 16 at 17:42
paw88789
28.2k12248
answered Jul 16 at 17:42
paw88789
28.2k12248
28.2k12248
add a comment |Â
add a comment |Â
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As long as $a>2$ or $b$ is composite, one can just write down a factor of $a^b-1$.
– Lord Shark the Unknown
Jul 16 at 17:44
...but even if $a>2$ and $b$ is prime, $a^b - 1$ can be composite.
– David G. Stork
Jul 16 at 18:55