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A107312 Primes p such that p + 2 and p^2 + 2^2 are primes. 1

%I #16 Sep 08 2022 08:45:18

%S 3,5,17,137,347,827,2087,2687,3557,3917,4517,4967,5477,5657,5867,6827,

%T 7457,7547,7877,8087,8537,8597,10037,10427,10937,12107,12377,13397,

%U 13877,16067,17837,17987,19427,19697,20507,20717,20807,22367,22637

%N Primes p such that p + 2 and p^2 + 2^2 are primes.

%C Primes are lesser twins. Except a(1) and a(2), all a(n) == 7(mod 10).

%H Edward Jiang, <a href="/A107312/b107312.txt">Table of n, a(n) for n = 1..1000</a>

%p select(p -> isprime(p) and isprime(p+2) and isprime(p^2+4), [seq(2*i+1,i=1..10000)]); # _Robert Israel_, Aug 11 2014

%t Select[Prime[Range[3000]], PrimeQ[ #+2]&&PrimeQ[ #^2+4]&]

%o (Magma) [p: p in PrimesUpTo(25000)| IsPrime(p+2) and IsPrime(p^2+4)] // _Vincenzo Librandi_, Jan 29 2011

%o (PARI) a(n)=isprime(n) && isprime(n+2) && isprime(n^2+4) \\ _Edward Jiang_, Aug O8 2014

%Y Cf. A045637.

%K nonn

%O 1,1

%A _Zak Seidov_, May 21 2005

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Last modified April 25 08:27 EDT 2024. Contains 371964 sequences. (Running on oeis4.)