A038599 -id:A038599 - cp's OEIS frontend

A108701 Values of n such that n^2-2 and n^2+2 are both prime.

3, 9, 15, 21, 33, 117, 237, 273, 303, 309, 387, 429, 441, 447, 513, 561, 573, 609, 807, 897, 1035, 1071, 1113, 1143, 1233, 1239, 1311, 1563, 1611, 1617, 1737, 1749, 1827, 1839, 1953, 2133, 2211, 2283, 2589, 2715, 2721, 2955, 3081, 3093, 3453, 3549, 3555, 3621, 3723, 3807

Offset: 1

John L. Drost, Jun 19 2005

Since x^2 + 2 is divisible by 3 unless x is divisible by 3, all elements are 3 mod 6.

Intersection of A067201 and A028870. - Robert Israel, Sep 11 2014

			21 is on the list since 21^2 - 2 = 439 and 21^2 + 2 = 443 are primes.

David Wells, Prime Numbers, John Wiley and Sons, 2005, p. 219 (article:'Siamese primes')

Nathaniel Johnston, Table of n, a(n) for n = 1..8750
Raymond A. Beauregard and E. R. Suryanarayan, Square-plus-two primes, Mathematical Gazette 85(502) 90-1.

Subsequence of A016945.

Cf. A016945, A028870, A028873, A038599, A067201, A153974.

[n: n in [3..3600 by 6] | IsPrime(n^2-2) and IsPrime(n^2+2)];  // Bruno Berselli, Apr 15 2011

select(n -> isprime(n^2-2) and isprime(n^2+2), [seq(6*i+3,i=0..1000)]); # Robert Israel, Sep 11 2014

Select[Range[5000], PrimeQ[#^2 - 2] && PrimeQ[#^2 + 2] &] (* Alonso del Arte, Sep 11 2014 *)

is(n)=isprime(n^2-2)&&isprime(n^2+2) \\ Charles R Greathouse IV, Jul 02 2013

Terms corrected by Charles R Greathouse IV, Sep 11 2014

A154831 Numbers n such that n^4-2 is prime.

Original entry on oeis.org

3, 7, 11, 13, 21, 29, 39, 41, 43, 49, 53, 59, 73, 83, 85, 87, 95, 99, 101, 119, 129, 141, 143, 175, 181, 185, 189, 207, 217, 239, 241, 277, 279, 293, 311, 315, 323, 339, 343, 363, 367, 371, 375, 381, 389, 409, 421, 433, 435, 451, 473, 483, 497, 503, 507, 515

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 15 2009

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

Cf. A028870, A038599.

[n: n in [1..500] | IsPrime(n^4-2)]; // Vincenzo Librandi, Nov 26 2010

lst={};Do[p=n^4-2;If[PrimeQ[p],AppendTo[lst,n]],{n,0,7!}];lst
Select[Range[600],PrimeQ[#^4-2]&] (* Harvey P. Dale, May 20 2012 *)

is(n)=isprime(n^4-2) \\ Charles R Greathouse IV, Jul 02 2013

A153974 Numbers n such that n^3 - 3 is prime.

Original entry on oeis.org

2, 4, 8, 10, 14, 16, 26, 34, 38, 40, 74, 80, 106, 110, 116, 124, 136, 158, 178, 184, 190, 206, 224, 230, 238, 256, 274, 280, 316, 320, 338, 340, 386, 410, 428, 446, 458, 464, 470, 484, 496, 530, 544, 550, 556, 590, 626, 634, 644, 646, 674, 710, 718, 728, 730

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

nonn

2^3 - 3 = 5 is prime, 4^3 - 3 = 61 is prime, ...

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A028870, A028873, A038599, A108701, A153975.

[n: n in [2..500] | IsPrime(n^3-3)]; // Vincenzo Librandi, Nov 26 2010

a[n_]:=n^x-y;lst={};x=3;y=3;Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,0,6!}];lst
Select[Range[2, 1000], PrimeQ[#^3 - 3] &] (* G. C. Greubel, Sep 01 2016 *)

is(n)=isprime(n^3-3) \\ Charles R Greathouse IV, Feb 17 2017

First two terms 0,1, removed by Zak Seidov, Mar 14 2009

A154832 Primes p such that p^4-2 is also prime.

Original entry on oeis.org

3, 7, 11, 13, 29, 41, 43, 53, 59, 73, 83, 101, 181, 239, 241, 277, 293, 311, 367, 389, 409, 421, 433, 503, 587, 617, 647, 683, 757, 773, 811, 823, 839, 881, 907, 953, 1019, 1093, 1117, 1187, 1249, 1361, 1471, 1481, 1543, 1553, 1571, 1637, 1667, 1747, 1789, 1847

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 15 2009

nonn

Primes in A154831.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A028870, A038599, A154831

lst={};Do[p=n^4-2;If[PrimeQ[p],If[PrimeQ[n],AppendTo[lst,n]]],{n,0,7!}];lst
Select[Prime[Range[300]],PrimeQ[#^4-2]&] (* Harvey P. Dale, Nov 24 2018 *)

A154833 Numbers n such that n^5-2 is prime.

Original entry on oeis.org

3, 13, 31, 63, 93, 139, 181, 211, 229, 265, 271, 303, 325, 339, 343, 345, 411, 441, 519, 523, 531, 549, 555, 573, 619, 663, 675, 681, 693, 741, 751, 805, 819, 835, 853, 861, 945, 951, 969, 975, 993, 1063, 1071, 1095, 1119, 1143, 1275, 1281, 1305, 1329

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 15 2009

3^5-2=241 prime, 13^5-2=371291 prime,...

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

Cf. A028870, A038599, A154831, A154832.

[n: n in [1..500] | IsPrime(n^5-2)]; // Vincenzo Librandi, Nov 26 2010

lst={};Do[p=n^5-2;If[PrimeQ[p],AppendTo[lst,n]],{n,0,7!}];lst
Select[Range[2 10^3], PrimeQ[#^5 - 2] &] (* Vincenzo Librandi, Mar 20 2014 *)

is(n)=isprime(n^5-2) \\ Charles R Greathouse IV, Feb 17 2017

A154834 Primes p such that p^5 - 2 is also prime.

Original entry on oeis.org

3, 13, 31, 139, 181, 211, 229, 271, 523, 619, 751, 853, 1063, 1483, 1699, 2791, 3361, 3463, 3541, 3769, 4051, 4201, 4801, 4861, 4903, 5521, 5689, 5701, 6163, 6211, 6763, 6823, 6949, 7621, 8059, 8269, 8389, 8419, 8563, 8689, 8713, 9001, 9103, 9319, 10303

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 15 2009

nonn

Primes in A154833.

			3^5 - 2 = 241 is prime,
13^5 - 2 = 371291 is prime, ...

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A028870, A038599, A154831, A154832, A154833.

lst={};Do[p=n^5-2;If[PrimeQ[p],If[PrimeQ[n],AppendTo[lst,n]]],{n,0,7!}];lst
Select[Prime[Range[1300]],PrimeQ[#^5-2]&] (* Harvey P. Dale, Feb 09 2019 *)

A178251 Primes p such that p^3 - 2 is prime.

Original entry on oeis.org

19, 31, 37, 67, 109, 151, 211, 241, 277, 367, 439, 457, 619, 691, 727, 787, 859, 967, 1087, 1171, 1471, 1489, 1531, 1579, 1951, 2131, 2287, 2791, 2851, 2971, 3061, 3319, 3511, 3547, 3559, 3739, 4129, 4357, 4447, 4507, 4591, 4651, 4789, 4801, 4831, 4951

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 24 2010

			6857 = prime(882) = 19^3 - 2, 19 = prime(8) is 1st term.
29789 = prime(3228) = 31^3 - 2, 31 = prime(11) is 2nd term.

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

Cf. A000040, A000578, A038599, A038600, A144953.

[p: p in PrimesUpTo(5000) | IsPrime(p^3-2)]; // Vincenzo Librandi, Nov 17 2010

Select[Prime[Range[10000]], PrimeQ[#^3 - 2] &] (* Vincenzo Librandi, Mar 20 2014 *)

list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(p^3-2), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 08 2016

a = list(p for p in primes(10000) if is_prime(p**3-2)) # D. S. McNeil, May 25 2010

Base tag removed by D. S. McNeil, May 25 2010

A038600 Primes of the form n^3 - 2.

Original entry on oeis.org

727, 3373, 6857, 19681, 29789, 50651, 300761, 753569, 970297, 1295027, 1771559, 2146687, 2460373, 3048623, 3442949, 4492123, 6539201, 6751267, 8120599, 8869741, 9393929, 10218311, 13997519, 17373977, 18609623, 19034161, 21253931

Offset: 1

Jeff Burch

nonn

			a(2) = 3373 = 15^3 - 2 = A038599(2)^3 - 2.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A038599.

lst={};Do[s=n^3;If[PrimeQ[p=s-2], AppendTo[lst, p]], {n, 6!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 26 2008 *)
Select[Range[300]^3-2,PrimeQ] (* Harvey P. Dale, Jul 18 2015 *)

Corrected and extended by Jud McCranie, Jan 04 2001

A154933 Numbers k such that k^6 - 2 is prime.

Original entry on oeis.org

3, 11, 17, 35, 37, 47, 49, 59, 67, 77, 99, 123, 127, 133, 139, 155, 161, 169, 173, 187, 195, 213, 225, 231, 237, 241, 245, 247, 253, 275, 279, 297, 319, 325, 367, 373, 381, 383, 385, 399, 411, 425, 431, 469, 507, 511, 523, 541, 545, 553, 569, 585, 589, 609

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A028870, A038599, A154831, A154832, A154833, A154834.

lst={};Do[p=n^6-2;If[PrimeQ[p],AppendTo[lst,n]],{n,1,7!}];lst

isA154933(n) = isprime(n^6-2) \\ Michael B. Porter, Oct 06 2009

a(1) = 0 removed by Amiram Eldar, Apr 04 2020

A154935 Numbers n such that n^7-2 is prime.

Original entry on oeis.org

7, 15, 25, 87, 91, 99, 199, 211, 265, 337, 357, 361, 367, 405, 501, 511, 537, 595, 627, 685, 697, 771, 805, 841, 847, 861, 889, 931, 939, 979, 1035, 1047, 1081, 1125, 1135, 1177, 1225, 1231, 1287, 1315, 1321, 1387, 1425, 1497, 1501, 1627, 1741, 1795, 1807

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

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

Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154933, A154934.

[n: n in [1..500]|IsPrime(n^7-2)]; // Vincenzo Librandi, Nov 26 2010

lst={};Do[p=n^7-2;If[PrimeQ[p],AppendTo[lst,n]],{n,0,7!}];lst
Select[Range[2*10^3], PrimeQ[#^7 - 2] &] (* Vincenzo Librandi, Mar 20 2014 *)

is(n)=isprime(n^7-2) \\ Charles R Greathouse IV, Feb 17 2017

cp's OEIS Frontend

A108701 Values of n such that n^2-2 and n^2+2 are both prime.

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A154831 Numbers n such that n^4-2 is prime.

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A153974 Numbers n such that n^3 - 3 is prime.

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A154832 Primes p such that p^4-2 is also prime.

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A154833 Numbers n such that n^5-2 is prime.

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A154834 Primes p such that p^5 - 2 is also prime.

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A178251 Primes p such that p^3 - 2 is prime.

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