At 11:59 AM 1999/03/05 GMT, "Brian J Beesley" <[EMAIL PROTECTED]> wrote:
>> (Ken wrote)
>> Right. The odds heavily favor both mismatched residues being nonzero.
>> A zero residue at the last iteration is what indicates primality.
>
>Depends on what you mean. If a Mersenne number that has been
>tested once really is prime, but the test "went wrong", then we
>have a wrong result i.e. calling the number composite when it isn't.
I mean that nearly all mersenne numbers are nonprime even if the exponents
are prime, so of the numbers we bother to LLtest, when an error occurs,
the odds are 99%+ that it does not conceal an actual Mersenne prime.
And in the unusal case of a nonprime Mersenne number being erroneously
identified as prime, it would be multiply-checked and so the error caught,
rather than being announced as a prime.
>This is why double-checking is so important, if we want to find *all*
>the Mersenne primes for exponents up to a given limit.
I agree that double checking is important in an exhaustive search,
and that exhaustive search (rather than haphazard or opportunistic search)
is valuable.
>There *might* be one or two lurking somewhere in the mass of
>exponents which have only been tested once.
>>
>> >Also what causes the errors, bugs in the code?
>>
>> What I've seen most often is that prime95 and its relatives provide
>> early warning of unreliable hardware, whether cpu, RAM module, or
motherboard.
>
>Usually caused by overheating - failed CPU fan, poor ventilation or
>excessively hot environment, overclocking, poor thermal contact
>between processor substrate and heatsink ...
The sorts of things I've seen include, in systems with good cpu heat sinking,
multiple case fans, cpu fans properly installed and no overclocking:
mechanically ill-fitting case causing a system to be unreliable
unreliable single SIMM out of a set of 4
unreliable CPU chip
unreliable motherboard
whether these component-level problems were due to electrical stress
(power outages, spikes, brownouts, static), thermal stress (overheating
or too-frequent power on/off), or latent defects in manufacture is unknown.
Ken
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