A382481 a(n) is the number of primes less than 4^(n^2).

0, 2, 54, 23000, 203280221, 33483379603407, 96601075195075186855

Offset: 0

Author

Stefano Spezia, Mar 28 2025

Keywords

• nonn
• hard
• more

Comments

Thue's proof, that there exist infinitely many primes, shows also that n+1 is a lower bound for a(n) (see Ribenboim, 2004).

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 9-10.

Links

• a(n) = pi(4^(n^2)).
• a(n) = A007053(2*n^2). - _Amiram Eldar_, Mar 29 2025

Crossrefs

Cf. A000290, A000302, A000720, A007053, A060757.

Programs

Mathematica

a[n_]:=PrimePi[4^(n^2)]; Array[a,6,0]

Python

from sympy import primepi
def A382481(n): return primepi(1<<(n**2<<1)) # Chai Wah Wu, Mar 29 2025