(Soft Question) Largest known semiprimes with no known factors
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Is there a list, similar to prime numbers and probable primes, of the largest semiprimes with unknown factors? Is there a list of numbers that are either semiprime or prime, with no known factors? Is there literature on how to find large semi primes?
reference-request soft-question prime-numbers
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
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add a comment |
0
$begingroup$
Is there a list, similar to prime numbers and probable primes, of the largest semiprimes with unknown factors? Is there a list of numbers that are either semiprime or prime, with no known factors? Is there literature on how to find large semi primes?
reference-request soft-question prime-numbers
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
$endgroup$
$begingroup$
I feel like a list of "possible semiprimes" would likely be at least somewhat coincident with a list of possible primes, given that a large semiprime accordingly has large prime factors (so finding said factors would be difficult, thus rendering the number a possible candidate for either). As for finding large semiprimes, I feel the easiest method would just be to multiply two large known primes together, but I imagine you want something more elegant.
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– Eevee Trainer
Dec 8 '18 at 22:27
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Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest.
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– gammatester
Dec 8 '18 at 22:34
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It's unclear how one could be certain that a large number was a semiprime (as opposed to having three or more prime factors) without knowing the two prime factors which multiply to it.
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– Keith Backman
Dec 9 '18 at 2:33
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@KeithBackman Surprisingly, this seems to be possible. I heard from a construction of a number which could be proven to be semiprime without known factors (according to the claim, not even by the constructor himself). For huge number, this method is probably not feasible.
$endgroup$
– Peter
Dec 9 '18 at 14:11
add a comment |
0
0
0
$begingroup$
Is there a list, similar to prime numbers and probable primes, of the largest semiprimes with unknown factors? Is there a list of numbers that are either semiprime or prime, with no known factors? Is there literature on how to find large semi primes?
reference-request soft-question prime-numbers
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
$endgroup$
Is there a list, similar to prime numbers and probable primes, of the largest semiprimes with unknown factors? Is there a list of numbers that are either semiprime or prime, with no known factors? Is there literature on how to find large semi primes?
reference-request soft-question prime-numbers
reference-request soft-question prime-numbers
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
asked Dec 8 '18 at 22:20
Tejas RaoTejas Rao
30611
30611
$begingroup$
I feel like a list of "possible semiprimes" would likely be at least somewhat coincident with a list of possible primes, given that a large semiprime accordingly has large prime factors (so finding said factors would be difficult, thus rendering the number a possible candidate for either). As for finding large semiprimes, I feel the easiest method would just be to multiply two large known primes together, but I imagine you want something more elegant.
$endgroup$
– Eevee Trainer
Dec 8 '18 at 22:27
$begingroup$
Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest.
$endgroup$
– gammatester
Dec 8 '18 at 22:34
$begingroup$
It's unclear how one could be certain that a large number was a semiprime (as opposed to having three or more prime factors) without knowing the two prime factors which multiply to it.
$endgroup$
– Keith Backman
Dec 9 '18 at 2:33
$begingroup$
@KeithBackman Surprisingly, this seems to be possible. I heard from a construction of a number which could be proven to be semiprime without known factors (according to the claim, not even by the constructor himself). For huge number, this method is probably not feasible.
$endgroup$
– Peter
Dec 9 '18 at 14:11
add a comment |
$begingroup$
I feel like a list of "possible semiprimes" would likely be at least somewhat coincident with a list of possible primes, given that a large semiprime accordingly has large prime factors (so finding said factors would be difficult, thus rendering the number a possible candidate for either). As for finding large semiprimes, I feel the easiest method would just be to multiply two large known primes together, but I imagine you want something more elegant.
$endgroup$
– Eevee Trainer
Dec 8 '18 at 22:27
$begingroup$
Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest.
$endgroup$
– gammatester
Dec 8 '18 at 22:34
$begingroup$
It's unclear how one could be certain that a large number was a semiprime (as opposed to having three or more prime factors) without knowing the two prime factors which multiply to it.
$endgroup$
– Keith Backman
Dec 9 '18 at 2:33
$begingroup$
@KeithBackman Surprisingly, this seems to be possible. I heard from a construction of a number which could be proven to be semiprime without known factors (according to the claim, not even by the constructor himself). For huge number, this method is probably not feasible.
$endgroup$
– Peter
Dec 9 '18 at 14:11
$begingroup$
I feel like a list of "possible semiprimes" would likely be at least somewhat coincident with a list of possible primes, given that a large semiprime accordingly has large prime factors (so finding said factors would be difficult, thus rendering the number a possible candidate for either). As for finding large semiprimes, I feel the easiest method would just be to multiply two large known primes together, but I imagine you want something more elegant.
$endgroup$
– Eevee Trainer
Dec 8 '18 at 22:27
$begingroup$
I feel like a list of "possible semiprimes" would likely be at least somewhat coincident with a list of possible primes, given that a large semiprime accordingly has large prime factors (so finding said factors would be difficult, thus rendering the number a possible candidate for either). As for finding large semiprimes, I feel the easiest method would just be to multiply two large known primes together, but I imagine you want something more elegant.
$endgroup$
– Eevee Trainer
Dec 8 '18 at 22:27
$begingroup$
Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest.
$endgroup$
– gammatester
Dec 8 '18 at 22:34
$begingroup$
Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest.
$endgroup$
– gammatester
Dec 8 '18 at 22:34
$begingroup$
It's unclear how one could be certain that a large number was a semiprime (as opposed to having three or more prime factors) without knowing the two prime factors which multiply to it.
$endgroup$
– Keith Backman
Dec 9 '18 at 2:33
$begingroup$
It's unclear how one could be certain that a large number was a semiprime (as opposed to having three or more prime factors) without knowing the two prime factors which multiply to it.
$endgroup$
– Keith Backman
Dec 9 '18 at 2:33
$begingroup$
@KeithBackman Surprisingly, this seems to be possible. I heard from a construction of a number which could be proven to be semiprime without known factors (according to the claim, not even by the constructor himself). For huge number, this method is probably not feasible.
$endgroup$
– Peter
Dec 9 '18 at 14:11
$begingroup$
@KeithBackman Surprisingly, this seems to be possible. I heard from a construction of a number which could be proven to be semiprime without known factors (according to the claim, not even by the constructor himself). For huge number, this method is probably not feasible.
$endgroup$
– Peter
Dec 9 '18 at 14:11
add a comment |
1 Answer
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It doesn't exist. Any area of rectangle which sides are prime is a semiprime.
answered Dec 9 '18 at 2:24
usirousiro
32539
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1
$begingroup$
There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime.
$endgroup$
– Peter
Dec 9 '18 at 14:13
add a comment |
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1 Answer
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1 Answer
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$begingroup$
It doesn't exist. Any area of rectangle which sides are prime is a semiprime.
answered Dec 9 '18 at 2:24
usirousiro
32539
$endgroup$
1
$begingroup$
There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime.
$endgroup$
– Peter
Dec 9 '18 at 14:13
add a comment |
0
$begingroup$
It doesn't exist. Any area of rectangle which sides are prime is a semiprime.
answered Dec 9 '18 at 2:24
usirousiro
32539
$endgroup$
1
$begingroup$
There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime.
$endgroup$
– Peter
Dec 9 '18 at 14:13
add a comment |
0
0
0
$begingroup$
It doesn't exist. Any area of rectangle which sides are prime is a semiprime.
answered Dec 9 '18 at 2:24
usirousiro
32539
$endgroup$
It doesn't exist. Any area of rectangle which sides are prime is a semiprime.
answered Dec 9 '18 at 2:24
usirousiro
32539
answered Dec 9 '18 at 2:24
usirousiro
32539
answered Dec 9 '18 at 2:24
usirousiro
32539
answered Dec 9 '18 at 2:24
usirousiro
32539
32539
1
$begingroup$
There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime.
$endgroup$
– Peter
Dec 9 '18 at 14:13
add a comment |
1
$begingroup$
There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime.
$endgroup$
– Peter
Dec 9 '18 at 14:13
1
1
$begingroup$
There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime.
$endgroup$
– Peter
Dec 9 '18 at 14:13
$begingroup$
There are also infinite many primes, but nevertheless it makes sense to speak of the largest known prime.
$endgroup$
– Peter
Dec 9 '18 at 14:13
add a comment |
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I feel like a list of "possible semiprimes" would likely be at least somewhat coincident with a list of possible primes, given that a large semiprime accordingly has large prime factors (so finding said factors would be difficult, thus rendering the number a possible candidate for either). As for finding large semiprimes, I feel the easiest method would just be to multiply two large known primes together, but I imagine you want something more elegant.
$endgroup$
– Eevee Trainer
Dec 8 '18 at 22:27
$begingroup$
Maybe physics.open.ac.uk/~dbroadhu/cert/semgpch.gp is of interest.
$endgroup$
– gammatester
Dec 8 '18 at 22:34
$begingroup$
It's unclear how one could be certain that a large number was a semiprime (as opposed to having three or more prime factors) without knowing the two prime factors which multiply to it.
$endgroup$
– Keith Backman
Dec 9 '18 at 2:33
$begingroup$
@KeithBackman Surprisingly, this seems to be possible. I heard from a construction of a number which could be proven to be semiprime without known factors (according to the claim, not even by the constructor himself). For huge number, this method is probably not feasible.
$endgroup$
– Peter
Dec 9 '18 at 14:11