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Results tagged with Search options user 16322
2
votes
Most fast sieves are segmented, so you can get this in efficient amortized time. When you call to get the next segment, you may have to increase the auxiliary prime list, but that's a trivial amount …
answered Aug 31 '15 by DanaJ
0
votes
I believe your statement is the opposite of what happens. Passing the Miller-Rabin test for a given base means it will pass the Fermat test for the same base. In contrast, there are many composites …
answered Dec 25 '16 by DanaJ
1
vote
Your PatternSieve is what is called a wheel sieve, or the wheel optimization for the SoE and is mentioned at the SoE Wikipedia page. It's well known and used in all fast SoE implementations. See Whe …
answered Dec 20 '17 by DanaJ
1
vote
The cop-out but realistic answer for small inputs would be $O(1)$ for tiny inputs and roughly $O(\log n)$ below some finite threshold as it can be done as a binary search through a table of primes
answered Oct 12 '15 by DanaJ
1
vote
There are a number of modifications, but none of the improvements I'm aware of will get it remotely close to the speed of ECPP or APR-CL. For random 100-digit primes, the times for the fastest codes …
answered Dec 25 '16 by DanaJ
5
votes
References for the test: Pomerance, Selfridge, Wagstaff, "The Pseudoprimes to 25 x 10^9", July 1980. Page 1024-1025, Check if n is a strong probable prime base 2. Check whether n is a Lucas probable …
answered Jan 27 '17 by DanaJ
22
votes
Quick answer: Never, for practical purposes. It is not currently of any practical use. First, let's separate out "practical" compositeness testing from primality proofs. The former is good enoug …
answered Apr 2 '14 by DanaJ