Consider six consecutive positive integers. Show that there is a prime number that divides exactly one of them.
(In reply to
re: One conjecture dead, one still alive by JLo)
JLo:
Bertrand's postulate (which is proved) says that there is guaranteed to
be a prime between n+1 and 2n, for any n > 2. I don't believe
that this helps prove that there is a prime number that divides exactly
one of any n consecutive positive integers. It only proves that,
for n > 2, there is a prime number that divides exactly one of the n
consectutive integers starting with n+1. It doesn't, however, say
anything about sequences of n integers whose first number is > n+1.
For instance, consider n = 10.
Bertrand's postulate guarantees that there is a prime number that
divides exactly one of 11, 12, 13, ... 20. It doesn't help at all
if the sequence of 10 numbers starts with 12 or 13 or 1234789632.
Re Bertrand's postulate
