OFFSET
1,1
EXAMPLE
For j=0 1+1=2 is prime; also terms should be lesser-twin-primes
because of p^1+2^1=p+2=prime; 3rd and 4th conditions are as
follows: prime=p^2+4 and prime=16+p^4.
MATHEMATICA
{ta=Table[0, {100}], u=1}; Do[s0=2; s1=Prime[j]+2; s2=4+Prime[j]^2; s4=16+Prime[j]^4; If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s4], Print[{j, Prime[j]}]; ta[[u]]=Prime[j]; u=u+1], {j, 1, 1000000}]
Select[Prime[Range[45000]], AllTrue[{2+#, 4+#^2, 16+#^4}, PrimeQ]&] (* Harvey P. Dale, Sep 18 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 01 2004
STATUS
approved