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p and p^2 + 6 are both prime.
9

%I #33 Feb 04 2024 01:13:48

%S 5,11,19,31,61,79,89,109,131,151,199,269,331,401,431,569,709,859,929,

%T 941,971,991,1039,1249,1319,1361,1409,1451,1531,1549,1559,1571,1601,

%U 1619,1699,1879,1901,1999,2069,2081,2089,2111,2179,2341,2399,2411,2621

%N p and p^2 + 6 are both prime.

%C The only common term with A137270 is 5. - _Zak Seidov_, Jun 16 2015

%C 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

%H Harry J. Smith, <a href="/A062718/b062718.txt">Table of n, a(n) for n=1..1000</a>

%t Select[Prime[Range[400]], PrimeQ[#^2 + 6] &] (* _Vincenzo Librandi_, Jun 16 2015 *)

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

%o (PARI) { 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

%o (Magma) [p: p in PrimesUpTo(3000) |IsPrime(p^2+6)]; // _Vincenzo Librandi_, Jun 16 2015

%Y Cf. A137270. - _Zak Seidov_, Jun 16 2015

%K nonn

%O 1,1

%A _Jason Earls_, Jul 14 2001