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Primes p such that 2*p^3 -+ 3 are also prime.
3

%I #28 Sep 08 2022 08:45:51

%S 2,13,1223,2357,4013,4027,4507,5903,8713,9623,10663,11717,12757,12983,

%T 13883,15877,16103,16787,16823,16883,18097,22697,23357,24677,26107,

%U 27953,28603,30313,31327,34147,35617,35933,41183,44893,46687,46817,48247,50417,52963,54083

%N Primes p such that 2*p^3 -+ 3 are also prime.

%C Intersection of A153507 and A243630. - _Felix Fröhlich_, Nov 27 2019

%H Harvey P. Dale and K. D. Bajpai, <a href="/A174363/b174363.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)

%e For p=2, 2*2^3 -+ 3 = (13, 19), both prime, so 2 is a term of the sequence.

%e For p=13, 2*13^3 -+ 3 = (4391, 4397), both prime, so 13 is a term of the sequence.

%p select(p -> andmap(isprime, [p, 2*p^3+3, 2*p^3-3]), [seq(p, p=1.. 10^5)]); # _K. D. Bajpai_, Nov 28 2019

%t Select[Prime[Range[5000]],And@@PrimeQ[2 #^3+{3,-3}]&] (* _Harvey P. Dale_, Jan 25 2013 *)

%o (Magma) [p: p in PrimesUpTo(100000)|IsPrime(2*p^3-3) and IsPrime(2*p^3+3)]

%o (PARI) forprime(p=1, 55000, if(ispseudoprime(2*p^3-3) && ispseudoprime(2*p^3+3), print1(p, ", "))) \\ _Felix Fröhlich_, Nov 27 2019

%Y Cf. A153507, A243630.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Mar 17 2010