A049409 -id:A049409 - cp's OEIS frontend

A065509 Primes p such that p^4 + p^3 + p^2 + p + 1 is prime.

2, 7, 13, 17, 23, 29, 43, 73, 79, 83, 127, 193, 227, 239, 263, 277, 337, 359, 373, 397, 439, 457, 479, 503, 557, 563, 617, 919, 967, 1009, 1129, 1187, 1249, 1297, 1327, 1429, 1493, 1553, 1579, 1657, 1663, 1979, 1987, 2069, 2243, 2383, 2617, 2663, 2789

Offset: 1

Vladeta Jovovic, Nov 26 2001

Primes in A049409. - Vincenzo Librandi, Aug 07 2010

The generated prime numbers are in A190527. - Bernard Schott, Dec 20 2012

			a(4) = 17 because 17 is prime and 17^4 + 17^3 + 17^2 + 17 + 1 = 88741 is prime.

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith).

Cf. A053182.

[n: n in [0..10000]| IsPrime(n) and IsPrime(n^4+n^3+n^2+n+1)] // Vincenzo Librandi, Aug 07 2010

f[n_]:=1+n+n^2+n^3+n^4; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst,p]], {n,6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 24 2009 *)
Select[Prime[Range[500]],PrimeQ[Total[#^Range[0,4]]]&] (* Harvey P. Dale, Apr 08 2017 *)

{ n=0; for (m=1, 10^9, p=prime(m); if (isprime(p^4 + p^3 + p^2 + p + 1), write("b065509.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 20 2009

{A065509_vec(N,p=1)=vector(N,i,until(isprime((p^5-1)\(p-1)),p=nextprime(p+1));p)} \\ M. F. Hasler, Mar 03 2020

A217073 Numbers k such that (k^23-1)/(k-1) is prime.

Original entry on oeis.org

10, 40, 82, 113, 127, 141, 170, 257, 275, 287, 295, 315, 344, 373, 442, 468, 609, 634, 646, 663, 671, 710, 819, 834, 857, 884, 894, 904, 992, 997, 1060, 1069, 1077, 1120, 1143, 1190, 1232, 1253, 1261, 1280, 1291, 1347, 1407, 1436, 1448, 1483, 1514, 1570, 1642

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..1700] |IsPrime((n^23 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 1700], PrimeQ[(#^23 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^23-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217074 Numbers k such that (k^29-1)/(k-1) is prime.

Original entry on oeis.org

6, 40, 65, 70, 114, 151, 221, 229, 268, 283, 398, 451, 460, 519, 554, 587, 627, 628, 659, 687, 699, 859, 884, 915, 943, 974, 986, 1101, 1120, 1159, 1176, 1212, 1223, 1297, 1312, 1322, 1337, 1390, 1409, 1415, 1446, 1477, 1508, 1592, 1636, 1691, 1800, 1802, 1803

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..2000] |IsPrime((n^29 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 2000], PrimeQ[(#^29 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^29-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217075 Numbers k such that (k^31-1)/(k-1) is prime.

Original entry on oeis.org

2, 14, 19, 31, 44, 53, 71, 82, 117, 127, 131, 145, 177, 197, 203, 241, 258, 261, 276, 283, 293, 320, 325, 379, 387, 388, 406, 413, 461, 462, 470, 486, 491, 534, 549, 569, 582, 612, 618, 639, 696, 706, 723, 746, 765, 767, 774, 796, 802, 877, 878, 903, 923, 981

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..1000] |IsPrime((n^31 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 1000], PrimeQ[(#^31 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^31-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217088 Numbers n such that (n^89-1)/(n-1) is prime.

Original entry on oeis.org

2, 114, 159, 190, 234, 251, 436, 616, 834, 878, 1008, 1049, 1060, 1062, 1118, 1472, 1689, 1792, 2282, 2334, 2463, 2494, 2584, 2672, 2706, 2739, 2747, 2872, 3145, 3210, 3312, 3427, 3429, 3442, 3652, 3855, 4000, 4074, 4104, 4287, 4419, 4493, 4635, 4675, 4708, 4839

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

Select[Range[2, 1000], PrimeQ[(#^89 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^89-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217076 Numbers k such that (k^37-1)/(k-1) is prime.

Original entry on oeis.org

61, 77, 94, 97, 99, 113, 126, 130, 134, 147, 161, 172, 187, 202, 208, 246, 261, 273, 285, 302, 320, 432, 444, 503, 523, 525, 563, 666, 680, 709, 740, 757, 787, 902, 962, 964, 969, 1013, 1109, 1165, 1186, 1219, 1351, 1528, 1587, 1660, 1698, 1710, 1754, 1811, 1972

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..2000] |IsPrime((n^37 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 2000], PrimeQ[(#^37 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^37-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217077 Numbers n such that (n^41-1)/(n-1) is prime.

Original entry on oeis.org

14, 53, 55, 58, 71, 76, 82, 211, 248, 271, 296, 316, 430, 433, 439, 472, 545, 553, 555, 596, 663, 677, 682, 746, 814, 832, 885, 926, 947, 959, 1048, 1121, 1146, 1175, 1207, 1300, 1302, 1390, 1404, 1445, 1466, 1541, 1650, 1699, 1702, 1706, 1756, 1757, 1782, 1902

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..2000] |IsPrime((n^41 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 2000], PrimeQ[(#^41 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^41-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217078 Numbers n such that (n^43-1)/(n-1) is prime.

Original entry on oeis.org

15, 21, 26, 86, 89, 114, 123, 163, 180, 310, 332, 377, 409, 438, 448, 457, 477, 526, 534, 556, 586, 612, 653, 665, 690, 692, 709, 760, 783, 803, 821, 848, 877, 899, 909, 942, 981, 1041, 1042, 1043, 1066, 1068, 1069, 1106, 1126, 1139, 1197, 1310, 1386, 1476, 1561

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..1600] |IsPrime((n^43 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 1600], PrimeQ[(#^43 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^43-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217079 Numbers n such that (n^47-1)/(n-1) is prime.

Original entry on oeis.org

5, 17, 19, 55, 62, 75, 89, 98, 99, 132, 172, 186, 197, 220, 268, 278, 279, 288, 439, 443, 496, 579, 583, 587, 742, 777, 825, 911, 966, 1003, 1029, 1155, 1202, 1267, 1377, 1461, 1472, 1473, 1530, 1562, 1634, 1682, 1705, 1783, 1848, 1852, 1885, 1900, 1943, 1957

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..2000] |IsPrime((n^47 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 2000], PrimeQ[(#^47 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^47-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

A217080 Numbers n such that (n^53-1)/(n-1) is prime.

Original entry on oeis.org

24, 45, 60, 165, 235, 272, 285, 298, 307, 381, 416, 429, 623, 799, 858, 924, 929, 936, 1034, 1067, 1076, 1130, 1223, 1243, 1327, 1488, 1592, 1594, 1659, 1673, 1676, 1678, 1762, 1873, 1917, 1928, 1997, 2110, 2117, 2141, 2166, 2231, 2243, 2293, 2338, 2380, 2420

Offset: 1

Tim Johannes Ohrtmann, Sep 26 2012

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002384, A049409, A100330, A162862, A217070-A217089.

[n: n in [2..2450] |IsPrime((n^53 - 1) div (n - 1))]; // Vincenzo Librandi, Sep 28 2012

Select[Range[2, 2500], PrimeQ[(#^53 - 1)/(# - 1)] &] (* T. D. Noe, Sep 26 2012 *)

is(n)=isprime((n^53-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

More terms from T. D. Noe, Sep 26 2012

cp's OEIS Frontend

A065509 Primes p such that p^4 + p^3 + p^2 + p + 1 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

A217073 Numbers k such that (k^23-1)/(k-1) is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A217074 Numbers k such that (k^29-1)/(k-1) is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A217075 Numbers k such that (k^31-1)/(k-1) is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A217088 Numbers n such that (n^89-1)/(n-1) is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A217076 Numbers k such that (k^37-1)/(k-1) is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A217077 Numbers n such that (n^41-1)/(n-1) is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A217078 Numbers n such that (n^43-1)/(n-1) is prime.