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-   -   Wilson-prime search practicalities (https://www.mersenneforum.org/showthread.php?t=16028)

rajula 2011-09-18 10:47

60e to 70e done. Three new near Wilson primes found after the first one I already reported:

[CODE]64643245189 -1-21p
66966581777 -1+91p
67133912011 -1+9p[/CODE]

Reserving 250e9 to 270e9.

Jeff Gilchrist 2011-09-18 11:27

[QUOTE=rajula;271945]60e to 70e done. Three new near Wilson primes found after the first one I already reported:[/QUOTE]

You picked a good range, so far all dry up here at this end.

Jeff Gilchrist 2011-09-20 12:24

I'm now reserving:
[B]270e9 to 300e9[/B]

And new discovery
[CODE]231939720421 -1+41p[/CODE]

R.D. Silverman 2011-09-20 13:44

[QUOTE=Jeff Gilchrist;272134]I'm now reserving:
[B]270e9 to 300e9[/B]

And new discovery
[CODE]231939720421 -1+41p[/CODE][/QUOTE]

Please reduce my ignorance by explaining the notation.

Jeff Gilchrist 2011-09-20 13:44

Now that we are getting up into higher numbers the memory usage is going up a lot. Trying to do 3e9 range with 45M primes is pushing over 4GB a process now. In order to run 2 processes at the same time I'm going to have to start cutting down to smaller ranges again.

Jeff Gilchrist 2011-09-20 13:49

[QUOTE=R.D. Silverman;272144]Please reduce my ignorance by explaining the notation.[/QUOTE]

(p-1)! == -1+k*p mod p^2 for abs(k) <= 100

p=231939720421
k=41

MrRepunit 2011-09-22 07:52

I completed the range 160e9-200e9, found no near Wilson prime.

Reserving the range 300e9-340e9.

jasonp 2011-09-22 15:55

[QUOTE=R.D. Silverman;272144]Please reduce my ignorance by explaining the notation.[/QUOTE]
You probably have pieced it together already, but the idea is to quantify the 'closeness' to a Wilson prime by expressing the factorial in base p. The smaller the p multiple the closer to being -1 mod p^2.

R.D. Silverman 2011-09-22 16:42

[QUOTE=jasonp;272403]You probably have pieced it together already, but the idea is to quantify the 'closeness' to a Wilson prime by expressing the factorial in base p. The smaller the p multiple the closer to being -1 mod p^2.[/QUOTE]

Note that 'closeness' as defined here conflicts with the notion of closeness
over the p-adics.

rogue 2011-09-22 17:50

[QUOTE=R.D. Silverman;272408]Note that 'closeness' as defined here conflicts with the notion of closeness over the p-adics.[/QUOTE]

Do you mean that jason used the term "closeness" incorrectly?

Could you elaborate on your statement? I don't understand what you mean when you say "closeness over the p-adics". I presume that is something different than what is referred to here as "special instance".

R.D. Silverman 2011-09-22 19:18

[QUOTE=rogue;272415]Do you mean that jason used the term "closeness" incorrectly?

Could you elaborate on your statement? I don't understand what you mean when you say "closeness over the p-adics". I presume that is something different than what is referred to here as "special instance".[/QUOTE]

Serre's "A Course In Arithmetic" contains a good exposition of p-adic fields.
I can provide other references as well. I have neither the time (or the space!) in this forum to give a "P-adics 101" course.


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