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Reference.org
Prime-counting function
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the prime-counting function is the <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> counting the number of <a href="/facts/Prime_number/L20FLkgn">prime numbers</a> less than or equal to some <a href="/facts/Real_number/R02gw5Pb">real number</a> x. It is denoted by <i>π</i>(<i>x</i>) (unrelated to the <a href="/facts/Pi/vC0UBj1q">number π</a>). </p><p>A symmetric variant seen sometimes is <i>π</i>0(<i>x</i>), which is equal to <i>π</i>(<i>x</i>) − 1⁄2 if x is exactly a prime number, and equal to <i>π</i>(<i>x</i>) otherwise. That is, the number of prime numbers less than x, plus half if x equals a prime. </p>