LL test evaluating...
 

In LL test lots of iterations like [B]a^2-2 mod Mp[/B] must be calculated.
Does GIMPS compute this iterations using the exact precalculated value of
[B]Mp[/B] (consisted of 8-10M digits) or it use some others algorithms?

[QUOTE=VolMike;107927]In LL test lots of iterations like [B]a^2-2 mod Mp[/B] must be calculated.
Does GIMPS compute this iterations using the exact precalculated value of
[B]Mp[/B] (consisted of 8-10M digits) or it use some others algorithms?[/QUOTE]

Yes.

What do you mean?
Program uses precalculated value of Mp
Or
Program does't use value of Mp?

[QUOTE=VolMike;107931]What do you mean?
Program uses precalculated value of Mp
Or
Program does't use value of Mp?[/QUOTE]

Yes

[quote=VolMike;107927]In LL test lots of iterations like [B]a^2-2 mod Mp[/B] must be calculated.
Does GIMPS compute this iterations using the exact precalculated value of
[B]Mp[/B] (consisted of 8-10M digits) or it use some others algorithms?[/quote]VolMike,

Whenever the GIMPS software needs to use the explicit value [B]Mp[/B], it uses the exact precalculated multimillion-bit value.

However, when calculating [B]a^2-2 mod Mp[/B], it does not calculate the same way you or I would do a modular squaring operation such as 4*4 - 2 mod 5 (let's call that the pencil-and-paper method), but uses a different method. The method it uses does not involve the value of [B]Mp[/B] in the same way that the pencil-and-paper method does.

So it both does, and does not, use the precalculated value of M[sub]p[/sub], depending on what portion of the operation you examine.

werwer
 

Let's speak generally... Mathematics can evaluate a^b mod n without computing a^b value. Does somebody know algorithm to evaluate a^b mod (c^d-k) for positive integers a,b,c,d,k WITHOUT calculating c^d-k?

[QUOTE=VolMike;107946]Let's speak generally... Mathematics can evaluate a^b mod n without computing a^b value. Does somebody know algorithm to evaluate a^b mod (c^d-k) for positive integers a,b,c,d,k WITHOUT calculating c^d-k?[/QUOTE]

Yes.

Look into IBDWT (irrational base discreet weighted transform).

[QUOTE=Prime95;107950]Look into IBDWT (irrational base discreet weighted transform).[/QUOTE]

Not to be confused with the IBDWT = "Irritable Bowel Drug Workshop Thread"

Like the name implies, though, let's just keep it amongst ourselves.

[QUOTE=ewmayer;107957]Not to be confused with the IBDWT = "Irritable Bowel Drug Workshop Thread"

Like the name implies, though, let's just keep it amongst ourselves.[/QUOTE]

Or with the other IBDWT = "International Beer Drinking & Wine Tasting" :razz:
.

[QUOTE=rgiltrap;107963]Or with the other IBDWT = "International Beer Drinking & Wine Tasting" [/QUOTE]

No, whilst we support the spirit of imbibery which that connotes, that would be IBD&WT. We here at mersenneforum.org are acronymically strict.