Re: Is 5 more likely to be a primitive root?

"George Marsaglia" <geo@xxxxxxxxxxxx> writes:
Out of curiosity yesterday, while watching Wimbledon
on TV, I put to Maple the task of finding the
frequencies for which 2,3,5,6,7 are primitive roots
for the first 500000 primes.
....
500000, .3742220000, .3740240000, .3939620000, .3738140000, .3743180000

Taking that a bit further.

#p p #primrt ratio
2000000 32452909 787741 0.3938705000000000000000000000

We often use 3 in establishing Proth probable primes.
Would 5 be a better choice?

Maybe it depends on the test. If you use a SPRP test, then the
following ratio of numbers has 5 with a large enough order to
be suffice as an advocate for primality.

500000 7368817 374336 0.7486720000000000000000000000

Whereas for base=2, the figure is
500000 7368791 374103 0.7482060000000000000000000000

And for 3:
500000 7368811 374069 0.7481380000000000000000000000

which are all roughly equal.


I don't like the implications of that, so I won't state them.
There are some far smarter number theoretists here, who can
probably spread some enlightenment.

Phil
--
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.