PARI's commands

[3.14159]

Originally Posted by science_man_88

what as a prime or as a Mersenne number ?

Use your snippets to show that it is a prime Mersenne number.

[science_man_88]

Originally Posted by 3.14159

Use your snippets to show that it is a prime Mersenne number.

well 127-3 = 124 124/2 = 62 so index 62 of 002450 will be a number

the question becomes will that be a number contained in px+c.

p in this case seems to be a possible factor of 2^z-1.

find when it hits px+c. determine px+c from finding c as the first time 6np+/-p intersects 24m+7. in the case of a prime we would have to find a faster way as you'd have to check every possible factor 2kz+1<sqrt(2^z-1)

[science_man_88]

sorry only have to check primes of form 2kz+1<sqrt(2^z-1)

[3.14159]

Quick pondering: I wanted to make a quick program that would generate k's for k * n! + 1 that would give a certain prime divisor, along with a prime-numbered cofactor.
I have everything set.. But the only issue I have is: How to grab that Mod number..

Ex: Mod(-1, 71)/11! = 51
51 * 11! + 1 is divisible by 71.

PARI is only able to give it in the form Mod(51, 71).

Everything else (the forstep, etc.) is pretty much set, what hinders me is pretty much how to obtain the Mod number alone besides handwork.

Is there a way to get the Mod number on its own? Why didn't they simply do this instead:

>Mod(-1, 71)/(11!)
%1 = 51

[CRGreathouse]

Originally Posted by 3.14159

How to grab that Mod number.

lift() is what you want. Also of interest is centerlift().

Originally Posted by 3.14159

Why didn't they simply do this instead:

>Mod(-1, 71)/(11!)
%1 = 51

Because the correct answer is the set of numbers of the form 51 + 71k, which includes more than just 51. Also, pragmatically, it's common for further calculations to use the intmod rather than just its lift over the integers.

[science_man_88]

is there a TeX to Pari and vice versa converter there should be lol but then again it would be quick large again lol why do i come up with ideas that seem never able to be realized lol.

[CRGreathouse]

Originally Posted by science_man_88

is there a TeX to Pari and vice versa converter there should be lol but then again it would be quick large again lol why do i come up with ideas that seem never able to be realized lol.

There's the Pari command Strtex, which works passably well:

Strtex((x-2)^6)
%1 = "x^6\n - 12 x^5\n + 60 x^4\n - 160 x^3\n + 240 x^2\n - 192 x\n + 64"

[3.14159]

@CRG: I tried an example: Find multiples of 30! which have 727 as a smallest divisor, and a prime cofactor:

It only circularly printed 727.

Here is the code snippet:

em(x,n,a,b)=lift(Mod(-1,x)/(n));forstep(b=(lift(Mod(-1,x)/(n))),10^(a),x,if(isprime((b*n+1)/x), print(x)))

My guess is that it treats this section as "equal to 727": b=(lift(Mod(-1,x)/(n))),10^(a)

Let's see what happens when I change it to: b==(lift(Mod(-1,x)/(n))),10^(a). (Syntax error.)

[science_man_88]

Originally Posted by CRGreathouse

There's the Pari command Strtex, which works passably well:

Strtex((x-2)^6)
%1 = "x^6\n - 12 x^5\n + 60 x^4\n - 160 x^3\n + 240 x^2\n - 192 x\n + 64"

for me:

(13:16) gp > Strtex(sum(x=0,101,x))
%27 = "5151"

doesn't seem to cut it.

[CRGreathouse]

Originally Posted by science_man_88

for me:

(13:16) gp > Strtex(sum(x=0,101,x))
%27 = "5151"

doesn't seem to cut it.

sum(x=0,101,x) is 5151, so that's all that Strtex ever sees. Strtex can't tell what created the 5151.

And I'm sure it's not smart enough to deal with functions. Let me check...

Strtex(n->sum(x=0,n,x))
%1 = "(n)\\mapsto sum(x=0,n,x)"

Huh... not what I expected. So it can handle them in some weak sense, but it doesn't know how to translate Pari functions.

[3.14159]

Hmm.. I finally got it to print something, but it's all incorrect.