A226497 The number of primes of the form i^2+j^4 (A028916) <= 10^n.

2, 6, 28, 121, 583, 2724, 13175, 64551, 322110, 1621929, 8254127

Offset: 1

Author

Marek Wolf and Robert G. Wilson v, Jun 09 2013

Keywords

• nonn
• more

Comments

Even if a prime has more than one representation in the form i^2+j^4, it is only counted once.

Iwaniec and Friedlander have proved there is infinity of the primes of the form i^2+j^4.

Crossrefs

Cf. A028916, A226495, A226496 & A226498.

Programs

Mathematica

mx = 2^40; lst = {};  Do[a = i^2 + j^4; If[ PrimeQ[a], AppendTo[lst, a]], {i, Sqrt[mx]}, {j, Sqrt[Sqrt[mx - i^2]]}]; Table[ Length@ Select[ Union@ lst, # < 10^n &], {n, 12}]