

A091729


Norms of prime elements of Z[sqrt(5)].


4



5, 29, 41, 61, 89, 101, 109, 121, 149, 169, 181, 229, 241, 269, 281, 289, 349, 361, 389, 401, 409, 421, 449, 461, 509, 521, 541, 569, 601, 641, 661, 701, 709, 761, 769, 809, 821, 829, 881, 929, 941, 961, 1009
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OFFSET

1,1


COMMENTS

Consists of those primes congruent to 1, 5, 9 (mod 20) together with the squares of those primes congruent to 1, 3, 7, 9 (mod 20). Suppose n appears in this sequence. Then the number of prime elements of norm n is 2 if n is 5 or a square and 4 otherwise.


REFERENCES

David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.


LINKS



PROG

(PARI) list(lim)=my(v=List([5]), t); forprime(p=29, lim, t=p%20; if(t==1t==9, listput(v, p))); forprime(p=11, sqrtint(lim\1), t=p%20; if(t==11t==13t==17t==19, listput(v, p^2))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017


CROSSREFS

The sequence of norms of prime ideals in the ring Z[sqrt(5)] is A091727.


KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



