A Conjecture on Primes and a Step towards Justification*
نویسنده
چکیده
For example, all the Fermat primes are evil while all the Mersenne primes > 3 are odious. Using direct calculations up to 10 we noticed that among the primes not exceeding n the evil primes are never in majority except for the cases n = 5 and n = 6. Moreover, in the considered limits the excess of the odious primes is not monotone but increases on the whole with records on primes 2, 13, 41, 67, 79, 109, 131, 137, . . . Let π(x)(π(x)) denote the number of the evil (odious) primes not exceeding x. Put
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