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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.
1
7, 19, 23, 43, 71, 101
OFFSET
1,1
COMMENTS
Primes in A292348.
Conjecture: the sequence is finite.
Any further terms are > 10^12. - Lucas A. Brown, Oct 05 2024
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 *)
PROG
(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=', ')
CROSSREFS
KEYWORD
nonn,base,more,hard
AUTHOR
Alex Ratushnyak, Dec 07 2017
STATUS
approved