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A330363
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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.
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5
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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
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OFFSET
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-45,1
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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Table[(((((x+3)*x-1583)*x-9483)*x+401614)*x+2351352)*x/72-11351, {x, -45, 12}] (* Paolo Xausa, Mar 13 2024 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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sign,fini,full,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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