Thread: "Rare" Primes
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Old 2008-08-20, 03:03   #7
Jens K Andersen
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Feb 2006

E616 Posts

As hinted by a not entirely moronic Hungarian, it strongly depends on which "types" you allow. has some possibilities.

It's easy to construct rare prime forms by picking a quickly growing function with one or a few early primes. You mention Generalized Fermat 10^2^n+1, but there is no base b with more than 7 known primes b^2^n+1, and finding one with more than 10 looks very hard. The record is 7 for b=2072005925466 at

If you want relatively notable named forms then some candidates are at (look for comments like "only known").

In addition to your list of proven repunit primes, there are known probable primes for n = 49081, 86453, 109297, 270343.

There is no known Wall-Sun-Sun prime although infinitely many are expected to exist.
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