

A358980


Least prime in a string of exactly n consecutive primes with primitive root 2, or 0 if no such prime exists.


0



2, 19, 3, 173, 53, 523, 31883, 123637, 71899, 565589, 1241557, 1925501, 604829, 52003139, 410665589, 3448332373, 1250481059, 5352930581
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OFFSET

0,1


COMMENTS

Pollack shows, on GRH, that arbitrarily large members of this sequence exist. This works with any nonsquare primitive root aside from 1.  Charles R Greathouse IV, Mar 21 2024


LINKS



EXAMPLE

a(5) = 523 because 523 is the least prime in a string of 5 consecutive primes, {523, 541, 547, 557, 563} all having 2 as primitive root.


MATHEMATICA

Table[p=2; While[(k=0; While[PrimitiveRoot@p==2, k++; p=NextPrime[p]]; k)!=n, p=NextPrime@p]; NextPrime[p, k], {n, 0, 9}]


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



