login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A238136
Primes p such that p^4-p^3+1 and p^4-p^3-1 are also primes.
4
1429, 5827, 7411, 9601, 12601, 18457, 20011, 20521, 24919, 25999, 28591, 29947, 33211, 33349, 36037, 38149, 41227, 42649, 43579, 45307, 46099, 49999, 52057, 52387, 54319, 59107, 59197, 59629, 67891, 70951, 73477, 74761, 75037, 81157, 92041, 93607, 114889
OFFSET
1,1
LINKS
EXAMPLE
1429 is in the sequence because 1429, (1429^4-1429^3+1) and (1429^4-1429^3-1) are all primes.
MAPLE
KD := proc() local a, b, d; a:=ithprime(n); b:= a^4-a^3+1; d:=a^4-a^3-1; if isprime (b) and isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..20000);
MATHEMATICA
Select[Prime[Range[3000]], PrimeQ[#^4-#^3+1]&&PrimeQ[#^4-#^3-1]&]
c=0; a=2; Do[k=Prime[n]; If[PrimeQ[k^4-k^3+1] &&PrimeQ[k^4-k^3-1], c=c+1; Print[c, " ", k]], {n, 1, 2000000}];
pQ[n_]:=Module[{c=n^4-n^3}, AllTrue[c+{1, -1}, PrimeQ]]; Select[Prime[ Range[ 11000]], pQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 19 2014 *)
PROG
(PARI) s=[]; forprime(p=2, 120000, if(isprime(p^4-p^3+1) && isprime(p^4-p^3-1), s=concat(s, p))); s \\ Colin Barker, Feb 18 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Feb 18 2014
STATUS
approved