A050268 Primes of the form 36*k^2 - 810*k + 2753, listed in order of increasing parameter k >= 0.

2753, 1979, 1277, 647, 89, 359, 953, 1619, 2357, 3167, 4049, 5003, 6029, 7127, 8297, 9539, 10853, 12239, 13697, 15227, 16829, 18503, 20249, 22067, 23957, 25919, 27953, 30059, 32237, 34487, 36809, 41669, 44207, 46817, 49499, 52253

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy
• less

Comments

The sequence of primes of this form, in order of increasing size, would read: 89, 359, 647, 953, 1277, 1619, 1979, 2357, 2753, ... - M. F. Hasler, Jan 18 2015

The polynomial is a transformed version of the polynomial P(x) = 36*x^2 + 18*x - 1801 whose absolute value gives 45 distinct primes for -33 <= x <= 11, found by Ruby in 1989. In the present sequence only positive values of the polynomial are taken into account. A117081 provides also the negative function values. - Hugo Pfoertner, Dec 13 2019

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Jitender Singh, Prime numbers and factorization of polynomials, arXiv:2411.18366 [math.NT], 2024.
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

Crossrefs

Cf. A022464, A117081.

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is  36*n^2 - 810*n + 2753]; // Vincenzo Librandi, Dec 08 2011

Maple

t1:=[seq(36*n^2 - 810*n + 2753,n=0..100)]; t2:=[]; for i from 1 to nops(t1) do if isprime(t1[i]) then t2:=[op(t2),t1[i]]; fi; od: t2; # N. J. A. Sloane

Mathematica

Select[Table[36n^2-810n+2753,{n,0,2000}],PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)

PARI

select(isprime, vector(1000, n, 36*n^2-810*n+2753)) \\ Charles R Greathouse IV, Feb 14 2011

Extensions

Definition corrected by M. F. Hasler, Jan 18 2015