A137270 -id:A137270 - cp's OEIS frontend

A062718 p and p^2 + 6 are both prime.

5, 11, 19, 31, 61, 79, 89, 109, 131, 151, 199, 269, 331, 401, 431, 569, 709, 859, 929, 941, 971, 991, 1039, 1249, 1319, 1361, 1409, 1451, 1531, 1549, 1559, 1571, 1601, 1619, 1699, 1879, 1901, 1999, 2069, 2081, 2089, 2111, 2179, 2341, 2399, 2411, 2621

Offset: 1

Jason Earls, Jul 14 2001

nonn

The only common term with A137270 is 5. - Zak Seidov, Jun 16 2015

First cases of two, three and four consecutive primes are {2069,2081}, {3041,3049,3061} and {3403531,3403549,3403559,3403571}. - Zak Seidov, Jun 16 2015

Harry J. Smith, Table of n, a(n) for n=1..1000

Cf. A137270. - Zak Seidov, Jun 16 2015

[p: p in PrimesUpTo(3000) |IsPrime(p^2+6)]; // Vincenzo Librandi, Jun 16 2015

Select[Prime[Range[400]], PrimeQ[#^2 + 6] &] (* Vincenzo Librandi, Jun 16 2015 *)

je=[]; for(n=1,700, if(isprime(prime(n)^2+6),je=concat(je, prime(n)))); je

{ n=0; for (m=1, 10^9, if (isprime(prime(m)^2 + 6), write("b062718.txt", n++, " ", prime(m)); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 09 2009

A258992 Primes p such that p^2 - 8 is also prime.

Original entry on oeis.org

5, 7, 11, 17, 19, 23, 31, 37, 53, 67, 101, 103, 149, 163, 173, 191, 227, 229, 241, 257, 269, 271, 313, 347, 353, 359, 367, 373, 383, 431, 467, 479, 487, 523, 541, 563, 577, 599, 613, 619, 647, 653, 661, 733, 761, 773, 823, 829, 859, 863, 919, 941, 1061, 1087

Offset: 1

Zak Seidov, Jun 16 2015

nonn

The first appearances of 2..6 consecutive primes in the sequence are: {31,37}, {5, 7, 11}, {353, 359, 367, 373}, {1293199, 1293203, 1293233, 1293239, 1293247}, {3982031, 3982037, 3982057, 3982067, 3982073, 3982079}.

Initial terms of the sets of exactly 6 consecutive primes: {3982031, 5495989, 33057589, 255414437, 495180067, 558985507}.

			From _K. D. Bajpai_, Jun 18 2015: (Start)
a(3) = 11: both 11 and 11^2 - 8 = 113 are prime.
a(4) = 17: both 17 and 17^2 - 8 = 281 are prime.
(End)

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A062718, A137270.

[p: p in PrimesUpTo(5000) | IsPrime(p^2-8)];  // K. D. Bajpai, Jun 18 2015

Select[Prime[Range[5000]], PrimeQ[#^2-8]&]  (* K. D. Bajpai, Jun 18 2015 *)

lista(nn) = forprime(p=2, nn, if (isprime(p^2-8), print1(p, ", "))); \\ Michel Marcus, Jun 16 2015

A162905 Primes of form p^2-6, p also a prime.

Original entry on oeis.org

3, 19, 43, 163, 283, 523, 2203, 2803, 4483, 5323, 6883, 9403, 11443, 12763, 27883, 37243, 38803, 69163, 85843, 100483, 134683, 139123, 146683, 208843, 214363, 218083, 237163, 253003, 310243, 351643, 368443, 413443, 418603, 452923, 458323

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 16 2009

nonn

f[n_]:=n^2-6; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,f[p]]], {n,7!}];lst
#^2-6&/@Select[Prime[Range[2,200]],PrimeQ[#^2-6]&] (* Harvey P. Dale, May 21 2021 *)

a(n) = (A137270(n))^2-6.

Cross-reference turned into formula by R. J. Mathar, Jul 27 2009

cp's OEIS Frontend

A062718 p and p^2 + 6 are both prime.

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A258992 Primes p such that p^2 - 8 is also prime.

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A162905 Primes of form p^2-6, p also a prime.

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