>
> Since George Woltman found and announced the bug in V17 prime95 and its
> relatives, which invalidates Lucas-Lehmer tests started by V17 for p>2^22
> (=4194304) with a nonzero shift count, I've been thinking about some
> possibilities for making such bugs less likely to reach the general
> GIMPS user and to have less impact if it does.
...
> I propose the following be considered, for each future version released
> (and for the versions in heavy use currently):
...
> 4. Volunteers run randomly selected exponents LLtests and others run double-
> checks of the same exponents simultaneously. Random selection may hit
> a test case that's useful but was not identified as a separate case.
A double-check can be done on a different computer using a different
program. The problem is that the double-check can take a month for one
exponent. The probability of a software bug to show up in the first 100
iterations should be the same as the next 100. Instead of testing a few
select exponents completely and comparing residues, do 100 iterations,
say, on many of the numbers and compare the 100th iteration residues.
The final iteration may be a special case and should be checked carefully.
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