A292349 Pri-most primes: primes p such that the majority of bits in the binary representation of p satisfy the following: complementing this bit produces a prime number.

7, 19, 23, 43, 71, 101

Offset: 1

Author

Alex Ratushnyak, Dec 07 2017

Keywords

• nonn
• base
• more
• hard

Comments

Primes in A292348.

Conjecture: the sequence is finite.

Any further terms are > 10^12. - Lucas A. Brown, Oct 05 2024

Crossrefs

Cf. A000040, A137985, A292348.

Programs

Mathematica

Select[Prime@ Range[10^5], Function[n, Function[d, 2 Count[Array[FromDigits[#, 2] &@ MapAt[Mod[# + 1, 2] &, d, #] &, Length@ d], ?PrimeQ] > Length@ d]@ IntegerDigits[n, 2]]] (* _Michael De Vlieger, Dec 08 2017 *)

Python

from sympy import isprime, primerange
for i in primerange(1, 1000):
  delta = 0
  bit = 1
  while  bit <= i:
    if isprime(i^bit): delta += 1
    else:              delta -= 1
    bit*=2
  if delta > 0:  print(str(i), end=',')