A330363 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.

39300979, 32074681, 25874993, 20591567, 16122559, 12374209, 9260431, 6702413, 4628227, 2972449, 1675789, 684731, -48817, -567863, -910661, -1111031, -1198669, -1199447, -1135703, -1026521, -888001, -733519, -573977, -418043, -272381, -141871, -29819

Offset

-45,1

Comments

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.

Links

Hugo Pfoertner, Table of n, a(n) for n = -45..12

François Dress and Bernard Landreau, Polynômes de degré supérieur à 2 prenant beaucoup de valeurs premières, arXiv:1402.7312 [math.NT], 28 Feb 2014.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A272599 A105004 A216006 * A233754 A203895 A072237

Adjacent sequences: A330360 A330361 A330362 * A330364 A330365 A330366

Keyword

sign,fini,full,less

Author

Hugo Pfoertner, Dec 12 2019

Extensions

Name edited by M. F. Hasler, Mar 11 2024

Status

approved