A236951 Primes p such that p^4 + p +/- 1 are twin primes.
2, 1049, 1847, 1871, 2129, 2789, 5351, 10709, 11279, 13907, 14321, 17627, 27179, 27809, 29921, 30029, 31859, 37511, 39359, 40559, 40841, 43577, 46091, 46301, 58271, 62207, 62981, 66347, 66947, 68777, 72341, 75617, 79397, 85091, 86579
Offset: 1
Keywords
Examples
2 is prime and 2^4+2+1 (19) and 2^4+2-1 (17) are twin primes. Thus, 2 is a member of this sequence.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..900
Programs
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Magma
[p: p in PrimesUpTo(90000) | IsPrime(p^4+p-1) and IsPrime(p^4+p+1)]; // Vincenzo Librandi, Feb 14 2014
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Mathematica
Select[Prime[Range[100000]], PrimeQ[#^4 + # - 1] && PrimeQ[#^4 + # + 1]&] (* Vincenzo Librandi, Feb 14 2014 *)
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Python
import sympy from sympy import isprime {print(p) for p in range(10**6) if isprime(p) and isprime(p**4+p+1) and isprime(p**4+p-1)}
Comments