%I #25 Mar 13 2024 04:42:09

%S 39300979,32074681,25874993,20591567,16122559,12374209,9260431,

%T 6702413,4628227,2972449,1675789,684731,-48817,-567863,-910661,

%U -1111031,-1198669,-1199447,-1135703,-1026521,-888001,-733519,-573977,-418043,-272381,-141871,-29819

%N 58 consecutive function values of the prime generating polynomial P(x) = (1/72)*x^6 + (1/24)*x^5 - (1583/72)*x^4 - (3161/24)*x^3 + (200807/36)*x^2 + (97973/3)*x - 11351: abs(P(n)) is prime for -45 <= n <= 12.

%C As of 2014, this is the polynomial with rational coefficients that produces the most primes for a contiguous region of n. It was found by François Dress and Bernard Landreau, see the publication linked below. The complete list of 58 values is provided as b-file.

%H Hugo Pfoertner, <a href="/A330363/b330363.txt">Table of n, a(n) for n = -45..12</a>

%H François Dress and Bernard Landreau, <a href="https://arxiv.org/abs/1402.7312">Polynômes de degré supérieur à 2 prenant beaucoup de valeurs premières</a>, arXiv:1402.7312 [math.NT], 28 Feb 2014.

%t Table[(((((x+3)*x-1583)*x-9483)*x+401614)*x+2351352)*x/72-11351, {x, -45, 12}] (* _Paolo Xausa_, Mar 13 2024 *)

%o (PARI) (P(x)=(((((x+3)*x-1583)*x-9483)/2*x+200807)/12*x+97973)/3*x-11351); [isprime(abs(p=P(n)))*p | n<-[-45..12]] \\ _M. F. Hasler_, Mar 11 2024

%Y Cf. A121887, A330364 (absolute values sorted by size).

%K sign,fini,full,less

%O -45,1

%A _Hugo Pfoertner_, Dec 12 2019

%E Name edited by _M. F. Hasler_, Mar 11 2024