Letter | Published:

Number of Primes and Probability Considerations

Nature volume 150, pages 120121 (25 July 1942) | Download Citation



SEVERAL months ago Lord Cherwell1 directed attention to an apparent paradox which arises if one attempts to use probability considerations to determine the asymptotic density of prime numbers. The argument is this: The probability that a large number is not divisible by a prime p is 1/p. If we assume that such probabilities are independent for all pertinent trial divisors, we obtain as the density of primes near N2 the value ; the correct value, however, is .

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  1. 1.

    NATURE, 148, 436 (1941).

  2. 2.

    and , Acta Mathematica, 44, 36–37 (1923), especially footnote 4, p. 37.

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  1. Department of Physics, Harvard University, Cambridge, Massachusetts.

    • W. H. FURRY


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