PARI's commands - Page 27

3.14159 · 2010-08-11, 23:46

Random pseudoprime: 759932492170846988701 is pseudoprime to bases 2, 3, 5, 7, 11, and 13. By the way: Is there a world record for "largest composite pseudoprime"?

Also: I forgot how to write a Fermat pseudoprime generator.

CRGreathouse · 2010-08-12, 01:05

Quote:

Originally Posted by 3.14159

Random pseudoprime: 759932492170846988701 is pseudoprime to bases 2, 3, 5, 7, 11, and 13. By the way: Is there a world record for "largest composite pseudoprime"?

Not really, you can generate them essentially as large as you like.

Quote:

Originally Posted by 3.14159

Also: I forgot how to write a Fermat pseudoprime generator.

Depends on what you mean by "generator". Are you looking for a program that does the Fermat test? A program that generates all Fermat pseudoprimes in a range? A program that generates a Fermat pseudoprime at a given size? Something else?

3.14159 · 2010-08-12, 11:37

Quote:

Originally Posted by CRGreathouse

Not really, you can generate them essentially as large as you like.

I see.

Quote:

Originally Posted by CRGreathouse

Depends on what you mean by "generator". Are you looking for a program that does the Fermat test? A program that generates all Fermat pseudoprimes in a range? A program that generates a Fermat pseudoprime at a given size? Something else?

A program that generates the Fermat pseudoprimes in a given range, that are pseudoprime to user-selected bases. (No need for a code snippet, I eventually remembered how to write it and saved it in the text document, along with the other functions.

science_man_88 · 2010-08-12, 12:01

$24m= 6np+(p-7)\right m=px+c$
$24m=6np-(p+7)\right m=px+c ?$
$if(px+c==(4n-1)/3,(4\strike n -1)/3$
for all remaining n that create primes print(2*n+3) these are Mersenne prime exponents

get this CRG ?

3.14159 · 2010-08-12, 12:23

An interesting application error:
Whenever I input 25326001, it returns that it is a 7-SPRP, when it is in fact reported "composite" using base 7. I verified that it was an error on the app. Now I see that this is an unreliable app, as it returns results that are clearly wrong.

CRGreathouse · 2010-08-12, 13:10

Quote:

Originally Posted by 3.14159

A program that generates the Fermat pseudoprimes in a given range, that are pseudoprime to user-selected bases. (No need for a code snippet, I eventually remembered how to write it and saved it in the text document, along with the other functions.

Ah. Hard task!

CRGreathouse · 2010-08-12, 13:13

Quote:

Originally Posted by 3.14159

An interesting application error:
Whenever I input 25326001, it returns that it is a 7-SPRP, when it is in fact reported "composite" using base 7. I verified that it was an error on the app. Now I see that this is an unreliable app, as it returns results that are clearly wrong.

What script are you using to check? My isSPRP gives

Code:

>isSPRP(25326001,7)
%1 = 0

science_man_88 · 2010-08-12, 13:17

Quote:

Originally Posted by science_man_88

$24m= 6np+(p-7)\right m=px+c$
$24m=6np-(p+7)\right m=px+c ?$
$if(px+c==(4n-1)/3,(4\strike n -1)/3$
for all remaining n that create primes print(2*n+3) these are Mersenne prime exponents

get this CRG ?

sorry should be (4^n-1)/3 lol
oh and there shouldn't be 2 n equations lol.

CRGreathouse · 2010-08-12, 13:32

Quote:

Originally Posted by science_man_88

$24m= 6np+(p-7)\right m=px+c$
$24m=6np-(p+7)\right m=px+c ?$
$if(px+c==(4n-1)/3,(4\strike n -1)/3$
for all remaining n that create primes print(2*n+3) these are Mersenne prime exponents

get this CRG ?

Hmm. Unlike the diagrams, I feel like I'm close to understanding something. The first two lines are clearly related to your repeating theme,
$24m+7=p(6n\pm1)$ .

The lines themselves seem to be statements of the division algorithm. The first says that if 24m+1 is of the form p(6n+1), then p(6n+1)/24 = px + c, that is, p(6n+1) leaves a remainder of c when divided by p.

But wait, it doesn't matter which of the first two lines I choose -- px + c is always m. So the first two lines say that 24m+7 is composite (assuming that n > 0 and p > 1) and the third line says that m is (4n-1)/3.

OK, so m = (4n-1)/3 means 3m+1 = 4n, so the third line is saying that $m\equiv1\pmod4$ . So let m = 4k+1, then 3(4k+1)+1=4n, so that n = 3k + 1.

The original composite is then 24m+7 = 24(4k + 1) + 7 = 96k + 31 and the Mersenne non-exponent is 2n+3 = 2(3k+1)+1=6k+3.

And indeed yes, this is correct: if k is a positive integer, then 6k+3 is not a Mersenne exponent. But this won't remove all bad exponents, of course.

CRGreathouse · 2010-08-12, 13:34

Quote:

Originally Posted by science_man_88

sorry should be (4^n-1)/3 lol
oh and there shouldn't be 2 n equations lol.

Pity, since I just analyzed it without.

Re-write it with those corrections and I'll see what I can do.

science_man_88 · 2010-08-12, 13:39

$24m= 6tp+(p-7)\right m=px+c$
$24m=6tp-(p+7)\right m=px+c ?$
$if(px+c==(4^n-1)/3,(4^\strike n -1)/3$
for all remaining n that create primes print(2*n+3) these are Mersenne prime exponents.

2010-08-11, 23:46	#287
3.14159 May 2010 Prime hunting commission. 1680₁₀ Posts	Random pseudoprime: 759932492170846988701 is pseudoprime to bases 2, 3, 5, 7, 11, and 13. By the way: Is there a world record for "largest composite pseudoprime"? Also: I forgot how to write a Fermat pseudoprime generator. Last fiddled with by 3.14159 on 2010-08-12 at 00:09

2010-08-12, 12:01	#290
science_man_88 "Forget I exist" Jul 2009 Dumbassville 20C0₁₆ Posts	$24m= 6np+(p-7)\right m=px+c$ $24m=6np-(p+7)\right m=px+c ?$ $if(px+c==(4n-1)/3,(4\strike n -1)/3$ for all remaining n that create primes print(2n+3) these are Mersenne prime exponents get this CRG ? Last fiddled with by science_man_88 on 2010-08-12 at 12:57*

2010-08-12, 13:39	#297
science_man_88 "Forget I exist" Jul 2009 Dumbassville 8384₁₀ Posts	$24m= 6tp+(p-7)\right m=px+c$ $24m=6tp-(p+7)\right m=px+c ?$ $if(px+c==(4^n-1)/3,(4^\strike n -1)/3$ for all remaining n that create primes print(2n+3) these are Mersenne prime exponents. Last fiddled with by science_man_88 on 2010-08-12 at 13:43*

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2010-08-12, 12:23	#291
3.14159 May 2010 Prime hunting commission. 11010010000₂ Posts	An interesting application error: Whenever I input 25326001, it returns that it is a 7-SPRP, when it is in fact reported "composite" using base 7. I verified that it was an error on the app. Now I see that this is an unreliable app, as it returns results that are clearly wrong.