- Some of you might recall that I posted a while ago on
the Primeform list about some proving code I was
Thanks to some off-list input and a custom-built
sieve, I started the program hunting for extreme
3-Carmichaels (the form with the record most within
I looked at the form A*2*3*23*29*31*37*41*
(5*7*11*13*17*19)^125 + 1, to keep the density high.
300 million candidates sieved to 1.6 million. After
16 hours of testing at 28/sec, I had 35,000+ PRPs.
About 2/3 of the time was spent in the PRPing stage
(which would have taken PFGW about twice as long to
do). Two of the 350 PRPs that passed stage 2 also
passed stage 3. They are:
p^2+p-1 and (p^3+p^2-p+1)/2 are also prime. The three
terms have, respectively, 793, 1585, and 2377 digits,
so the extreme 3-Carmichaels have 4754.
I've started a larger run to at least get the smallest
term over 1000 digits. Developing...
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