Fully factored

[paulunderwood]

I think Xyzzy was referring to the status "PRP" on the mersenne.ca e.g. prp-13 -- there is nothing to show what has been proved prime.

[lycorn]

Yes, I think so.
There are several cofactors on that page, other than PRP-13, that could trivially be proven or disproven prime, and be listed as the actual factor(s), instead of just PRP-xxx.
E.g. PRP-18 and PRP-22 for M101 and M103 respectively.

[LaurV]

Ping James on PM, he's a busy guy, he doesn't read all threads. The "desire" is trivial to implement. He can use the full expansion where reasonable, and use Pxxx and PRPxxx where the expansion is not reasonable, to show prime or probable-prime status.

[James Heinrich]

Originally Posted by LaurV

Ping James on PM, he's a busy guy, he doesn't read all threads. The "desire" is trivial to implement. He can use the full expansion where reasonable, and use Pxxx and PRPxxx where the expansion is not reasonable, to show prime or probable-prime status.

Thanks to GP2 who "pinged" me, the PRP page now shows "fully factored" and P-<digits> where the cofactor has been proven prime and PRP-<digits> where it has not been proven. The list of provens is maintained manually, and I'm handing it over to GP2 to maintain for me

However, I need one bit of help: to display the expansion of P-<digits> into decimal representation I suspect I should use PARI/GP to calculate it for me, but I'm ignorant of the language. Give the exponent and decimal representation of one or more known factors, how do I get the decimal representation of the last cofactor?

[science_man_88]

Originally Posted by James Heinrich

Thanks to GP2 who "pinged" me, the PRP page now shows "fully factored" and P-<digits> where the cofactor has been proven prime and PRP-<digits> where it has not been proven. The list of provens is maintained manually, and I'm handing it over to GP2 to maintain for me

However, I need one bit of help: to display the expansion of P-<digits> into decimal representation I suspect I should use PARI/GP to calculate it for me, but I'm ignorant of the language. Give the exponent and decimal representation of one or more known factors, how do I get the decimal representation of the last cofactor?

the naive way I think would be just to divide out the known factors from the mersenne and get what the other one is. the only other way that comes to mind is something like storing the k value for the cofactor and generating it from that but I bet that also gets inefficient quickly.

[James Heinrich]

Originally Posted by science_man_88

the naive way I think would be just to divide out the known factors from the mersenne and get what the other one is

That's what I want to do, but am ignorant of the syntax.

[science_man_88]

Originally Posted by James Heinrich

That's what I want to do, but am ignorant of the syntax.

/ is division
\ is the integer part of the division
% is mod ( that or Mod(a,b)
* is times
- subtraction
+ addition

see more in the "PARI command" thread.

[James Heinrich]

Thanks, but can someone give me the actual command line please? If I try something like

2^97/11447

for M97 with known factor of 11447 it just spits back "158456325028528675187087900672/11447"

[science_man_88]

Originally Posted by James Heinrich

Thanks, but can someone give me the actual command line please? If I try something like

2^97/11447

for M97 with known factor of 11447 it just spits back "158456325028528675187087900672/11447"

that's because M97 = 2^97-1 not 2^97 if you replace / with \ you'll get the answer to the question how many times without exceeding 2^97 does this number divide ( since it divides 2^97-1 it's the same answer as (2^97-1)/11447)

[James Heinrich]

Originally Posted by science_man_88

that's because M97 = 2^97-1 not 2^97

Silly me.
((2^97)-1)/11447 does what I want.

[James Heinrich]

So now the PRP page will show "P-<digits>" for the last factor, if you click on it the decimal representation will be shown.