A078523 Primes of the form a^2 + b^6.

2, 5, 17, 37, 73, 89, 101, 113, 197, 233, 257, 353, 401, 577, 593, 677, 733, 829, 1129, 1153, 1213, 1289, 1297, 1433, 1601, 1753, 1913, 2089, 2273, 2917, 3089, 3137, 3229, 3313, 3433, 4093, 4177, 4217, 4289, 4357, 4457, 4721, 4937, 5393, 5477, 5689, 6121

Offset

1,1

Comments

Friedlander and Iwaniec prove that there are an infinite number of primes of the form a^2+b^4 (A028916). They speculate that the a^2+b^6 case can be proved by similar methods.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

John Friedlander and Henryk Iwaniec, Using a parity-sensitive sieve to count prime values of a polynomial, PNAS February 18, 1997 94 (4) 1054-1058.

Jori Merikoski, A Cubic analogue of the Friedlander-Iwaniec spin over primes, arXiv:2012.05675 [math.NT], 2020.

Example

73 = 3^2 + 2^6

Mathematica

maxN=10000; lst={}; Do[p=i^2+j^6; If[p<maxN&&PrimeQ[p], AppendTo[lst, p]], {i, maxN^(1/2)}, {j, maxN^(1/6)}]; lst=Union[lst]

Prog

(PARI) list(lim)=my(v=List([2]), b6, t); lim\=1; for(b=1, sqrtnint(lim-1, 6), b6=b^6; forstep(a=1+b%2, sqrtint(lim-b6), 2, if(isprime(t=a^2+b6), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Aug 18 2017

Crossrefs

Cf. A028916.

Sequence in context: A107630 A379619 A379517 * A078324 A240322 A346809

Adjacent sequences: A078520 A078521 A078522 * A078524 A078525 A078526

Keyword

easy,nonn

Author

T. D. Noe, Nov 26 2002

Status

approved