What is this supposed to return?

[QUOTE]What is this supposed to return?[/QUOTE]

If prime, the number itself. If it fails trial division, the smallest prime factor.

[QUOTE=3.14159;222373]If prime, the number itself. If it fails trial division, the smallest prime factor.[/QUOTE]

Then you need to change the last line of the program (other than the "};" of course). And what's it supposed to return if the number is composite without a known factor?

[QUOTE]Then you need to change the last line of the program (other than the "};" of course). And what's it supposed to return if the number is composite without a known factor?[/QUOTE]

It returns zero if it's a composite that passes. So there are no pseudoprimes.

Testing for c100: 317305983867984894552374513880330942325323897104138220309522782479794265138440652957829496038865542387
Result = 31 ms.

c200: 47 ms.
c400: 78 ms.
c800: 218 ms.
c1600: 702 ms.

p200: 47 ms.
p400: 94 ms.
p800: 219 ms.

[QUOTE=3.14159;222381]It returns zero if it's a composite that passes. So there are no pseudoprimes.[/QUOTE]

I'm not sure what that has to do with what I said. You wrote of the program:

[QUOTE=3.14159;222373]If prime, the number itself. If it fails trial division, the smallest prime factor.[/QUOTE]

But for 101 it returns 1, not 101.

[QUOTE]But for 101 it returns 1, not 101.[/QUOTE]

Ah. I figured that one out. It only returns the number itself whenever you specify a base. Pretty much, the prime test can handle anything that's ≤ 1k digits in a few seconds. For larger primes, Proth will do to generate such numbers.

≈ 2000 digits: Approximately 1 second.
≈ 1000 digits: About 0.28 seconds.
≈ 3000 digits: About 2.65 seconds.

Testing the second largest prime I have ever found: 94.25 seconds.

Great. It's suitable for small primes and mid-sized primes.

Also: It may return either: Mod(1, n), or Mod(n-1, n) for primes.

Params set: SPRP = Trial division + Miller-Rabin test (Primality confirmation: [URL="http://www.alpertron.com.ar/ECM.HTM"]Perform here[/URL]. Be warned: 900+ digits, it uses Miller-Rabin as a test, use this only for small integers. For larger cases, use PARI's isprime(n) function.)

WPRP = Fermat's primality test"

Hey: I thought of something:
I'm going to code the original 7-step test, and see by how much it is slower, in the long run. Tips?

Here's my long-winded guess:
[code]primetest(n) = {
if(ispower(n) == 1,print(1));
forprime(p=2,nextprime(500),
if(n%p==0,return(p))
);
if(Mod(b, n)^(n-1) == 1,print(n));
my(s=valuation(n-1,2),d=n>>s);
n = Mod(b, n)^d;
if (n == 1, return(1));
while(s--,
if (n == -1, return(1));
n = n^2;
);
n == -1
};[/code]

[QUOTE=3.14159;222383]Ah. I figured that one out. It only returns the number itself whenever you specify a base. Pretty much, the prime test can handle anything that's ≤ 1k digits in a few seconds. For larger primes, Proth will do to generate such numbers.

≈ 2000 digits: Approximately 1 second.
≈ 1000 digits: About 0.28 seconds.
≈ 3000 digits: About 2.65 seconds.

Testing the second largest prime I have ever found: 94.25 seconds.

Great. It's suitable for small primes and mid-sized primes.

Also: It may return either: Mod(1, n), or Mod(n-1, n) for primes.

Params set: SPRP = Trial division + Miller-Rabin test (Primality confirmation: [URL="http://www.alpertron.com.ar/ECM.HTM"]Perform here[/URL]. Be warned: 900+ digits, it uses Miller-Rabin as a test, use this only for small integers. For larger cases, use PARI's isprime(n) function.)

WPRP = Fermat's primality test"

Hey: I thought of something:
I'm going to code the original 7-step test, and see by how much it is slower, in the long run. Tips?

Here's my long-winded guess:
[code]primetest(n) = {
if(ispower(n) == 1,print(1));
forprime(p=2,nextprime(500),
if(n%p==0,return(p))
);
if(Mod(b, n)^(n-1) == 1,print(n));
my(s=valuation(n-1,2),d=n>>s);
n = Mod(b, n)^d;
if (n == 1, return(1));
while(s--,
if (n == -1, return(1));
n = n^2;
);
n == -1
};[/code][/QUOTE]

I may no nothing about the test but I'm pretty sure you don't have to have the ==1 part for ispower as it should just check it itself.

Testing.. Dammit. I have a syntax error. The error reads:
[code] *** Mod: incorrect type in Rg_to_Fl.[/code]

[QUOTE=3.14159;222400]Testing.. Dammit. I have a syntax error. The error reads:
[code] *** Mod: incorrect type in Rg_to_Fl.[/code][/QUOTE]

you also have what I pointed out with something extra than what's needed. I can't spot much else but I'm not good with PARI(especially the new stuff).

[QUOTE=3.14159;222383]Hey: I thought of something:
I'm going to code the original 7-step test, and see by how much it is slower, in the long run. Tips?[/QUOTE]

1. Don't print 1 when a power is found, instead return 0.
2. You can't raise b to a power mod n unless you know what b is. (I suggest adding an optional argument for b.)
3. Don't print n when Mod(b, n)^(n-1) == 1, instead return n.
4. Change the line n == -1 to an if statement returning either 0 or n.

I see four steps, not seven (power, trial division, Fermat test, M-R test). Also I suggest adding an addhelp explaining how the function works: you wouldn't want someone doing
[code]if(primetest(n), print(n" is prime"))[/code]
the way you've written it.

.. I can't code it altogether. It has to be done in separate tests for the original.