A237995 Primes p such that p^4 - p^3 - 1 is also prime.
2, 3, 5, 11, 17, 53, 59, 101, 103, 151, 157, 167, 193, 197, 239, 353, 379, 397, 419, 433, 467, 479, 503, 599, 641, 659, 661, 743, 787, 881, 907, 911, 983, 1049, 1109, 1123, 1153, 1201, 1229, 1291, 1307, 1373, 1399, 1429, 1531, 1601, 1621, 1663, 1747, 1753
Offset: 1
Keywords
Examples
5 is in the sequence because 5 is prime and 5^4 - 5^3 - 1 = 499 is also prime. 17 is in the sequence because 17 is prime and 17^4 - 17^3 - 1 = 78607 is also prime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..3700
Programs
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Maple
KD := proc() local a,b; a:= ithprime(n); b:= a^4-a^3-1;if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..400);
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Mathematica
c = 0; a = 2; Do[k = Prime[n]; If[PrimeQ[k^4 - k^3 - 1], c = c + 1; Print[c, " ", k]], {n, 100000}]; (* Bajpai *) Select[Prime[Range[200]], PrimeQ[#^4 - #^3 - 1] &] (* Alonso del Arte, Feb 17 2014 *) -
PARI
s=[]; forprime(p=2, 2000, if(isprime(p^4-p^3-1), s=concat(s, p))); s \\ Colin Barker, Feb 17 2014