Comments on: Narcissus prime in Python

By: A suffix prime — The Endeavour

A suffix prime — The Endeavour — Tue, 12 Mar 2013 22:20:14 +0000

[...] Narcissus prime Sonnet primes Limerick primes Prime telephone numbers Prime words [...]

By: Waldir

Waldir — Thu, 24 Jan 2013 01:24:21 +0000

This is a naive (and probably flawed) version for Julia:

require("bigint")
isprime( BigInt( strcat( repeat( "1808010808", 1560 ), "1" ) ) )

I assume it is flawed because I get a segmentation fault. In fact, even with prime numbers as "small" as 953467954114363 I get segfaults often, though when the it works, it takes over a minute.

By: SymPy « Ok, panico

SymPy « Ok, panico — Sat, 19 Jan 2013 08:46:29 +0000

[...] è partito, l’altro giorno, da un post di John D. Cook, questo: Narcissus prime in Python. Non ho rifatto il calcolo di John, troppo lungo, ma SymPy l’ho installato subito. Per Ubuntu [...]

By: Sol

Sol — Sat, 19 Jan 2013 01:12:14 +0000

Perl6 version: say ("1808010808" x 1560 ~ "1").Int.is-prime; On Rakudo Perl 6 it runs in 4 hours.

By: Glyph

Glyph — Fri, 18 Jan 2013 23:09:18 +0000

Arguably, this is the cause of the problem.

By: Charlie

Charlie — Thu, 17 Jan 2013 20:04:01 +0000

This one is deterministic, but when running it under pypy on my rig, it finishes in under 18 minutes. Surely a probabilistic algorithm can finish much faster.
def modpower(b, e, n): '''Iterative method for Fermat's Test, O(n^3) instead of exponential. From Computations in Number Theory Using Python: A Brief Introduction, Jim Carlson, March 2003''' result = 1 s = b q = e while q > 0: #r = q % 2 r = q & 1 if r == 1: result = result * s % n # print q, r, s, result s = s * s % n #q = q/2 q = q >> 1 return result

def is_prime(n): return modpower(2, n-1, n) == 1

By: TheBlackCat

TheBlackCat — Thu, 17 Jan 2013 18:25:31 +0000

In addition to the other issues, there are a couple things I notice in the sympy code:

1. It tests if the target number is a pseudoprime after running the mathematical test. I would think this would be a relatively fast operation so maybe it could be done first. This isn’t related to this issue, though.

2. It doesn’t use any threading. Tests for different bases could be run simultaneously.

3. The actual test function does some of the exact same calculations multiple times for each base, even though the calculations in question are independent of the base.

4. If I am reading it correctly, the test function could skip the tests as long as b**2 is lower than n-1, since that case b**2%n will never equal n-1.

By: TheBlackCat

TheBlackCat — Thu, 17 Jan 2013 18:00:32 +0000

The last paragraph in this article describes the algorithm in Mathematica:

http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html

It appears they use similar versions of one algorithm (although not identical), while mathematica also uses another algorithm.

By: Kyle

Kyle — Thu, 17 Jan 2013 16:36:24 +0000

For reference: https://github.com/sympy/sympy/blob/master/sympy/ntheory/primetest.py

By: John

John — Thu, 17 Jan 2013 14:50:45 +0000

Kyle: I don’t know. They’re probably using different algorithms, different big integer implementations, etc. I don’t know whether either algorithm is deterministic: probabilistic algorithms are much faster, but could possibly be wrong.

By: Kyle

Kyle — Thu, 17 Jan 2013 14:37:23 +0000

Any reason as to why? Is Python’s isprime more expensive? Can it be improved?