Vincenzo Manto

[Draft] A396945

Created: 12/31/1 | Author: Vincenzo Manto , Jun 11 2026

Primes p for which floor(p / Pi) is prime.

Many pairs of twin primes (p, p+2) belong to the sequence and map to the same prime, because the gap 2/Pi is often too small to cross an integer boundary.The probability that a prime p belongs to the sequence is asymptotically proportional to 1/log(p), thus this sequence is predictable and may be infinite.

Sequence Chart

Graph of A396945

Data

7,11,17,23,37,41,43,61,73,131,137,149,167,193,211,251,263,281,307,337,401,431,433,439,563,569,571,601,607,619,701,733,751,809,827,829,853,883,967,997,1061,1091,1093,1097,1109,1129,1153,1193,1223,1249,1319,1361,1381,1451

Computational Implementations

PYTHON

from sympy import pi, isprime, primerange
import math
print([p for p in primerange(2, 1500) if isprime(math.floor(p / pi.evalf()))])

Cross-References

See also OEIS entries: Cf. A000040, A079592, A000796, A032615.