A079594 Primes p such that floor(p^Pi) is prime.

3, 73, 109, 131, 277, 397, 617, 739, 857, 911, 1109, 1181, 1237, 1453, 1889, 1999, 2239, 2383, 2393, 2621, 2767, 2801, 2903, 2953, 3259, 3319, 3323, 3967, 4127, 4243, 4603, 5051, 5237, 5407, 5419, 5573, 5749, 5843, 6091, 6317, 6679, 6701, 7691, 7949, 8297, 8377

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

floor(2^Pi)=8, which is not prime.
floor(3^Pi)=31, which is prime, so a(1)=3.
The next smallest prime p for which floor(p^Pi) is prime is 73, for which floor(73^Pi)=714169, so a(2)=73.

Maple

q:= p-> andmap(isprime, [p, floor(p^Pi)]):
select(q, [$2..9000])[];  # Alois P. Heinz, Aug 21 2025

Mathematica

For[i = 1, i < 10000, If[PrimeQ[IntegerPart[Prime[i]^Pi]] == True, Print[Prime[i]]]; i++ ]

Crossrefs

Cf. A000796, A074218, A079595.

Sequence in context: A392803 A139888 A271628 * A089922 A259848 A041279

Adjacent sequences: A079591 A079592 A079593 * A079595 A079596 A079597

Keyword

nonn

Author

Neil Fernandez, Jan 27 2003

Status

approved