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Adding to Eric Naslund's comment: Let $\pi(x)$ denote the number of primes less than $x$, then Montgomery & Vaughan proved that
$$ \pi(x+y)-\pi(x) \le 2 \pi(y)$$
for $x\ge 2$$x\ge 1$ and $y\ge 1.$$y\ge 2.$
Adding to Eric Naslund's comment: Let $\pi(x)$ denote the number of primes less than $x$, then Montgomery & Vaughan proved that
$$ \pi(x+y)-\pi(x) \le 2 \pi(y)$$
for $x\ge 2$ and $y\ge 1.$
Adding to Eric Naslund's comment: Let $\pi(x)$ denote the number of primes less than $x$, then Montgomery & Vaughan proved that
$$ \pi(x+y)-\pi(x) \le 2 \pi(y)$$
for $x\ge 1$ and $y\ge 2.$
Adding to Eric Naslund's comment: Let $\pi(x)$ denote the number of primes less than $x$, then Montgomery & Vaughan proved that
$$ \pi(x+y)-\pi(x) \le 2 \pi(y)$$
for $x\ge 2$ and $y\ge 1.$
