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Topic: Combining Primes
Replies: 81   Last Post: Aug 19, 2013 1:12 PM

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Phil Carmody

Posts: 2,219
Registered: 12/7/04
Re: Combining Primes
Posted: Aug 19, 2013 12:43 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

jim <jim@jimkeener.com> writes:
> Is there any way to combine 2 primes to get a larger prime, either
> guarantying the primality of the result or with a quick test for the
> primality?


Kinda - there are ways to combine 2 primes to get a larger prime, on
the assumption that you're permitted bounded iteration in the
generation of the result.

If your known primes are p and q, then test k*p*q+1 for small even k
(k < (pq)^2). Once you've found a probable prime, you can then use a
N-1 test to quickly prove it to be prime.

So having 2 smaller primes (even 1 will do) gives you a quicker
*proof* of the primality, but it won't have sped up the finding of the
candidate. For this to be significant, you must understand and care
about the difference between probable primes and proven primes.

Phil
--
If "law-abiding citizens have nothing to fear" from privacy-invading
technologies and policies, then law-abiding governments should have
nothing to fear from whistleblowers.


Date Subject Author
8/10/13
Read Combining Primes
jim
8/10/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
Sandy
8/10/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
Sandy
8/10/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
Sandy
8/10/13
Read Re: Combining Primes
Bart Goddard
8/10/13
Read Re: Combining Primes
Peter Percival
8/10/13
Read Re: Combining Primes
Bart Goddard
8/11/13
Read Re: Combining Primes
Peter Percival
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Bart Goddard
8/11/13
Read Re: Combining Primes
Peter Percival
8/11/13
Read Re: Combining Primes
fom
8/10/13
Read Re: Combining Primes
antani
8/10/13
Read Re: Combining Primes
Bart Goddard
8/10/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
Bart Goddard
8/10/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
Bart Goddard
8/10/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Peter Percival
8/11/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Peter Percival
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Peter Percival
8/10/13
Read Re: Combining Primes
Virgil
8/10/13
Read Re: Combining Primes
Peter Percival
8/10/13
Read Re: Combining Primes
rossum
8/10/13
Read Re: Combining Primes
John
8/10/13
Read Re: Combining Primes
Helmut Richter
8/10/13
Read Re: Combining Primes
Helmut Richter
8/19/13
Read Re: Combining Primes
Phil Carmody
8/10/13
Read Re: Combining Primes
antani
8/11/13
Read Re: Combining Primes
Helmut Richter
8/10/13
Read Re: Combining Primes
Sandy
8/10/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Sandy
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Sandy
8/10/13
Read Re: Combining Primes
William Elliot
8/10/13
Read Re: Combining Primes
namducnguyen
8/10/13
Read Re: Combining Primes
William Elliot
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
William Elliot
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
William Elliot
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Sandy
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Sandy
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Sandy
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Sandy
8/11/13
Read Re: Combining Primes
namducnguyen
8/12/13
Read Re: Combining Primes
Sandy
8/12/13
Read Re: Combining Primes
Bart Goddard
8/13/13
Read Re: Combining Primes
Shmuel (Seymour J.) Metz
8/11/13
Read Re: Combining Primes
Sandy
8/19/13
Read Re: Combining Primes
Phil Carmody
8/11/13
Read Re: Combining Primes
Sandy
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
Sandy
8/13/13
Read Re: Combining Primes
Shmuel (Seymour J.) Metz
8/11/13
Read Re: Combining Primes
Pubkeybreaker
8/11/13
Read Re: Combining Primes
Peter Percival
8/11/13
Read Re: Combining Primes
fom
8/11/13
Read Re: Combining Primes
Brian Q. Hutchings
8/12/13
Read Re: Combining Primes
namducnguyen
8/12/13
Read Re: Combining Primes
namducnguyen
8/12/13
Read Re: Combining Primes
Peter Percival
8/13/13
Read Re: Combining Primes
Shmuel (Seymour J.) Metz
8/12/13
Read Re: Combining Primes
Peter Percival
8/11/13
Read Re: Combining Primes
namducnguyen
8/11/13
Read Re: Combining Primes
namducnguyen
8/12/13
Read Re: Combining Primes
namducnguyen
8/12/13
Read Re: Combining Primes
Peter Percival
8/19/13
Read Re: Combining Primes
Phil Carmody

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