Hi,
At 11:33 PM 3/2/99 +0000, Tony Forbes wrote:
>George Woltman <[EMAIL PROTECTED]> writes
>>Finding an error in the first LL test is not rare. I've said about 1 in
>>200 are incorrect. When the entire 1,400,000 - 2,000,000 range has
>>been double-checked I'll perform some more rigorous analysis of the
>>reliability of first-time LL results.
>
>This is slightly worrying.
A prelimiary analysis for your consumption:
Looking at prime95 and mprime results between 1,400,000 and 2,000,000:
There are 220 residues that have been proven wrong.
These were produced by 99 different users.
78 of these results were produced by version 17.
Of these 78, 53 did not report any errors, 3 reported illegal sumout errors,
and 22 reported the more serious roundoff and mismatched sum errors.
There are 27490 verified results.
12665 of these were produced by version 17.
Of these 12665, 12493 did not report any errors, 120 reported illegal sumout
errors, and 53 reported the more serious errors.
There are 2204 unverified results on 1909 exponents. This does not mean
that there are 295 more bad results. It is not uncommon to have 2 or 3
prime95 results but the exponent is not considered verified because one
of the results must be from version 17.
So what does the above mean? Feel free to draw your own conclusions
and post them to the list.
I think the error rate is somewhere between 78 in 12665
for version 17 and 142 in 14825 for pre-v17 results. Actually, the error rate
will be higher because of the pending triple-checks in the unverified results.
It looks like my estimate of 1 in 200 was too optimistic.
It also looks like the illegal sumout errors do not seriously impact
reliability, but the other errors mean you have only a 70% chance of
producing a good result.
>The number of CPU cycles for performing the
>LL-test for exponent n is approximately proportional to n^2*log(n).
>Assuming, maybe rather naively, that the risk of computer error is
>proportional to the number of CPU cycles,
I personally think this is too naive an assumption. I think a PC is
either good at producing accurate results or it isn't. Obviously, the
longer the test, the more likely an error will creep in - but my gut tells
me this is a relatively minor effect.
>Do we have any statistics for the larger exponents?
No. There have been a few scattered double-checks, but nothing
statistically significant.
Best regards,
George
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