The S992 base is the first base where Iam seeing only Proth RES64 entries not RES64 and OLD64. Iam a bit confused.

The stderr.txt also contains

[B]Starting Proth prime test[/B]

Never seen this before.

If anybody know why this happened tell me pls.

S814 tested to n=100k (50-100k)

nothing found

Results emailed - Base released

Reserving S841 to n=100k (25-100k) for BOINC

Reserving S912 to n=100k (25-100k) for BOINC

S871 tested to n=100k (50-100k)

6 primes found, 22 remain

19512*871^53106+1 is prime!
15726*871^64212+1 is prime!
6472*871^69628+1 is prime!
20382*871^70537+1 is prime!
18682*871^77041+1 is prime!
7050*871^94061+1 is prime!

Results emailed - Base released

S992 tested to n=100k (25-100k)

6 primes found, 45 remain

64*992^25886+1 is prime!
185*992^26147+1 is prime!
229*992^26230+1 is prime!
151*992^52836+1 is prime!
182*992^77755+1 is prime!
295*992^93988+1 is prime!

Results emailed - Base released

Reserving S894 to n=100k (50-100k) for BOINC

[QUOTE=rebirther;397279]The S992 base is the first base where Iam seeing only Proth RES64 entries not RES64 and OLD64. Iam a bit confused.

The stderr.txt also contains

[B]Starting Proth prime test[/B]

Never seen this before.

If anybody know why this happened tell me pls.[/QUOTE]
Proth RES64's mean that a base 2 primality test was performed. Normally you only see this for base 2 Proth numbers (k*2^n+1 - we call them Sierpinski bases here in the context of conjectures), and its counterpart "LLR RES64" for base 2 Riesel numbers (k*2^n-1). However, some bases other than 2 are of a special mathematical form that allows them to be converted to base 2. For instance:

[tex]k\cdot4^n-1[/tex] (Riesel base 4 number) = [tex]k\cdot 2^{2n} -1[/tex] (equivalent Riesel base 2 number)

Powers of 2, as in the above example with base 4, are simple examples of this. Others, such as S992, have a slightly more complicated relationship to their equivalent base 2 form, but the basic idea is the same.

LLR automatically detects many of these special forms and converts the number to base 2 before doing the test. In the past, this was a huge advantage (because base 2 tests were much faster); now, the speed difference is not so huge, but I think there's still a small difference. Also, base 2 LLR/Proth tests produce a full primality proof, whereas other bases are only a PRP (probable primality) test; when a PRP is found in another base, a secondary N-1/N+1 test has to then be performed to prove that the number is actually prime. (LLR handles this automatically - that's why tests take way more than twice as long if the number turns out to be prime, because it's actually doing two tests, the second of which is much longer.)

So, long story short...that's why you're getting "Proth RES64" for S992. The numbers are being converted to base 2 and tested there. There's nothing to worry about, assuming your lresults.txt parser can handle the fact that LLR outputs the results in base 2 (not the original base). :smile:

With LLR it is necessary for k<2^n. I assume proth tests are the same. With base 992, k*992^n+1 can be rearranged as (k*31^n)*2^(5*n)+1. In many cases (k*31^n) will be less than 2^(5*n) and that is causing tests to be done as proth tests.

In terms of the speed of the calculations, if this was treated as base 2 then k would be too large and it would have to use a generic method. Using base 992 would probably be faster as k would hopefully be small enough to use a specialised method.

Thx mdettweiler and henryzz for the explanations. Looking forward :smile:

Reserving S787 to n=100k (25-100k) for BOINC

Reserving R722 to n=100k (50-100k) for BOINC

S841 tested to n=100k (25-100k)

13 primes found, 20 remain

17172*841^25396+1 is prime!
13048*841^29664+1 is prime!
3966*841^32150+1 is prime!
20022*841^36372+1 is prime!
16972*841^37229+1 is prime!
14368*841^38949+1 is prime!
22086*841^40618+1 is prime!
5572*841^40777+1 is prime!
3580*841^67127+1 is prime!
15012*841^73029+1 is prime!
3346*841^73208+1 is prime!
9822*841^75757+1 is prime!
10956*841^96215+1 is prime!

Results emailed - Base released