Integers Relatively Prime to the First n Primes

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The probability that a prime number does not divide a natural number is
. Hence, the probability that a natural number is relatively prime to all primes less than
equals
. Legendre proved that the large
limit of this product is zero, meaning that the probability that a large random integer is a prime approaches zero. This Demonstration computes the probability that an integer is coprime with each of the first
primes.
Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA
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Riemann's zeta function is defined by . Legendre's theorem states that
.
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