

A058220


Ultrauseful primes: smallest k such that 2^(2^n)  k is prime.


7



1, 3, 5, 15, 5, 59, 159, 189, 569, 105, 1557, 2549, 2439, 13797, 25353, 5627, 24317, 231425, 164073
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OFFSET

1,2


COMMENTS

2^(2^16)  5627 was found by Joel Levy in Feb 2004.  Donovan Johnson, Sep 13 2008
Corresponding numbers to entries a(1) to a(12) are proven primes, higher terms are probable primes.  Matthias Baur, Mar 17 2020


LINKS



FORMULA



EXAMPLE

For n = 3, we see that 2^(2^3) = 2^8 = 256, which is clearly not prime.
256  1 = 255 = 3 * 5 * 17, so a(3) is not 1.
256  2 = 254 = 2 * 127, so a(3) is not 2 either.
256  3 = 253 = 11 * 23, so a(3) is not 3 either.
256  5 = 251, which is prime, so a(3) = 5.


MATHEMATICA

ultraUseful[n_] := Module[{x = 2^(2^n)}, x  NextPrime[x, 1]]; Array[ultraUseful, 17] (* Harvey P. Dale, Jun 04 2011 *)


CROSSREFS



KEYWORD

nonn,hard,nice,more


AUTHOR



EXTENSIONS



STATUS

approved



