A126893 -id:A126893 - cp's OEIS frontend

A066386 Numbers k such that k^6 + 1091 is prime.

0, 3906, 4620, 5166, 5376, 5460, 8190, 13020, 13986, 14490, 17934, 19740, 19950, 20664, 23226, 24654, 29736, 30114, 31206, 33516, 33600, 34104, 34314, 40320, 41286, 44016, 45066, 46116, 47754, 48300, 59850, 62244, 63420, 65310, 66864

Offset: 1

Harvey P. Dale, Dec 23 2001

D. Shanks, Solved and unsolved problems in number theory, Chelsea NY, 1985, p. 222, ex. 162.
D. Shanks, A low density of primes, Jour. Recreational Math. 5 (1971) 272-5.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 151 (Rev. ed. 1997)
Roozbeh Hazrat, Mathematica: A Problem-Centered Approach, Springer 2010, pp. 42, 172

Harry J. Smith, Table of n, a(n) for n = 1..1000
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 1091
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Cf. A161998, A126893, A119276.

Select[Range[100000], PrimeQ[ #^6 + 1091] &]

{ n=0; for (m=0, 10^9, if (isprime(m^6 + 1091), write("b066386.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 13 2010

0 added by Zak Seidov, Jan 26 2009

A126894 Numbers k such that k^12 + 4094 is prime.

Original entry on oeis.org

170625, 181545, 233415, 490035, 492765, 552825, 591045, 642915, 885885, 921375, 1262625, 1358175, 1481025, 1743105, 1748565, 1901445, 2029755, 2062515, 2073435, 2119845, 2193555, 2302755, 2532075, 2761395, 2764125, 2772315

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

Ribenboim P., 1996. The Little Book of Big Primes. Springer Verlag.

Cf. A066386, A126893, A126895.

[n: n in [0..4000] | IsPrime(n^12+4094)] // Vincenzo Librandi, Nov 23 2010

Select[Range[1000000], PrimeQ[#^12 + 4094] &]

is(n)=isprime(n^12+4094) \\ Charles R Greathouse IV, Feb 20 2017

More terms from Vincenzo Librandi, Mar 26 2010

A161998 Numbers n such that n^6 + 272 is prime.

Original entry on oeis.org

2163, 2541, 2667, 4011, 5187, 5733, 5985, 7119, 7371, 7707, 8547, 10017, 10731, 12579, 13041, 13125, 13293, 14007, 14679, 15855, 16317, 16401, 16863, 17283, 19131, 19383, 20139, 20475, 21021, 21357, 22197, 22995, 23457, 23667, 24591, 25053, 25389, 25641

Offset: 1

Arkadiusz Wesolowski, Jun 24 2009

nonn

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 272

Cf. A007519, A163592, A066386, A126893, A119276.

[n : n in [1..25641 by 2] | IsPrime(n^6+272)]; // Arkadiusz Wesolowski, Mar 05 2011

Select[Range[1, 25641, 2], PrimeQ[#^6 + 272] &] (* Arkadiusz Wesolowski, Mar 05 2011 *)

forstep(n=1, 25641, 2, if(isprime(n^6+272), print1(n, ", "))); \\ Arkadiusz Wesolowski, Mar 05 2011

A119276 Values of n such that n^6 + 29450922301244534 is prime.

Original entry on oeis.org

63693, 64785, 70455, 90993, 100107, 104475, 110103, 110817, 117957, 122325, 125055, 134127, 140343, 167685, 183183, 228585, 242235, 242445, 247527, 252735, 256095, 262983, 264243, 281463, 293685, 298053, 308133, 310485, 314475, 320565

Offset: 1

Eric W. Weisstein, May 12 2006

nonn

Carlos Rivera, Puzzle 275
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Cf. A161998, A066386, A126893.

Select[Range[350000],PrimeQ[#^6+29450922301244534]&] (* Harvey P. Dale, Mar 12 2016 *)

A126895 Numbers n such that (1365n)^12+4094 is prime.

Original entry on oeis.org

125, 133, 171, 359, 361, 405, 433, 471, 649, 675, 925, 995, 1085, 1277, 1281, 1393, 1487, 1511, 1519, 1553, 1607, 1687, 1855, 2023, 2025, 2031, 2207, 2259, 2387, 2495, 2673, 2749, 2851, 2957, 3057, 3067, 3251, 3271, 3277, 3355, 3401, 3599, 3701, 3763

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

A126894(n)/1365

Ribenboim P., 1996. The Little Book of Big Primes. Springer Verlag.

Cf. A066386, A126893, A126894.

Select[Range[1,3801,2],PrimeQ[(1365#)^12+4094]&] (* Harvey P. Dale, Aug 03 2018 *)

is(n)=isprime((1365*n)^12+4094) \\ Charles R Greathouse IV, May 22 2017

A122131 Numbers n such that n^12 + 488669 is prime.

Original entry on oeis.org

616980, 764400, 933660, 1051050, 1730820, 1758120, 2467920, 3093090, 3164070, 3461640, 3696420, 3890250, 3923010, 3950310, 4051320, 4075890, 4196010, 4286100, 4324320, 4337970, 4389840, 4556370, 4561830, 4720170, 4793880

Offset: 1

Eric W. Weisstein, Aug 21 2006

When n is odd the polynomial produces even values, so it is trivially composite. When n ends in 2, 4, 6, or 8 then n^12 ends in 6, so the polynomial produces values ending in 5, again composite. Hence all the values in this sequence are divisible by 10. - Dmitry Kamenetsky, Nov 08 2016

By Fermat's Little Theorem the polynomial is divisible by 2, 3, 5, 7 and 13 when n is not divisible by these primes. Hence all the values in the sequence are divisible by the product of these primes, 2730. - Chun Lok Yiu, Mar 14 2022

Paulo Ribenboim, The Little Book of Big Primes, Springer Verlag, 1996.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 138 terms from Vincenzo Librandi)
Dan Ismailescu and Yunkyu James Lee, Polynomially growing integer sequences all whose terms are composite, arXiv:2501.04851 [math.NT], 2025. See p. 2.
Eric Weisstein's World of Mathematics, Bouniakowsky Conjecture
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Cf. A066386, A126893, A126894, A126897.

[n: n in [0..10^7] | IsPrime(n^12+488669)]; // Vincenzo Librandi, May 03 2014

a = {}; Do[If[PrimeQ[x^12 + 488669], AppendTo[a, x]], {x, 616979, 10000000}]; a (* Artur Jasinski, Dec 31 2006 *)
Select[Range[10^7], PrimeQ[#^12 + 488669] &] (* Vincenzo Librandi, May 03 2014 *)

is(n)=isprime(n^12+488669) \\ Charles R Greathouse IV, Jun 06 2017

Edited by N. J. A. Sloane, May 07 2007

A163592 Numbers n such that n^6 + 545 is prime.

Original entry on oeis.org

84, 1302, 10584, 11382, 12012, 12558, 13356, 15498, 19362, 20286, 20496, 22092, 23142, 23772, 25452, 26418, 26502, 26544, 28644, 29274, 29778, 31374, 31962, 35406, 36876, 37338, 39522, 40152, 40488, 41286, 42924, 43428, 45108, 46116, 47754, 47796, 48678

Offset: 1

Arkadiusz Wesolowski, Aug 01 2009

nonn

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 545

Cf. A133870, A161998, A066386, A126893, A119276.

[n : n in [0..48678 by 2] | IsPrime(n^6+545)]; // Arkadiusz Wesolowski, Mar 05 2011

Select[Range[0, 48678, 2], PrimeQ[#^6 + 545] &] (* Arkadiusz Wesolowski, Mar 05 2011 *)

forstep(n=0, 48678, 2, if(isprime(n^6+545), print1(n, ", "))); \\ Arkadiusz Wesolowski, Mar 05 2011

A126897 Numbers n such that (2730n)^12+488669 is prime.

Original entry on oeis.org

226, 280, 342, 385, 634, 644, 904, 1133, 1159, 1268, 1354, 1425, 1437, 1447, 1484, 1493, 1537, 1570, 1584, 1589, 1608, 1669, 1671, 1729, 1756, 1779, 2221, 2399, 2424, 2462, 2501, 2544, 2829, 2831, 2871, 2938, 2944, 3037, 3070, 3184, 3208, 3254, 3256

Offset: 1

Artur Jasinski, Dec 31 2006

A122131(n)/2730

Ribenboim P., 1996. The Little Book of Big Primes. Springer Verlag.

Cf. A066386, A126893, A126894, A126895, A122131.

Select[Range[3300],PrimeQ[(2730#)^12+488669]&] (* Harvey P. Dale, Dec 03 2022 *)

is(n)=isprime((2730*n)^12+488669) \\ Charles R Greathouse IV, Jun 13 2017

cp's OEIS Frontend

A066386 Numbers k such that k^6 + 1091 is prime.

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A126894 Numbers k such that k^12 + 4094 is prime.

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A161998 Numbers n such that n^6 + 272 is prime.

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A119276 Values of n such that n^6 + 29450922301244534 is prime.

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A126895 Numbers n such that (1365n)^12+4094 is prime.

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A122131 Numbers n such that n^12 + 488669 is prime.

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Magma

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A163592 Numbers n such that n^6 + 545 is prime.

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Magma

Mathematica

PARI

A126897 Numbers n such that (2730n)^12+488669 is prime.

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