Abstract
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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References
NATURE, 148, 436 (1941).
Hardy and Littlewood, Acta Mathematica, 44, 36–37 (1923), especially footnote 4, p. 37.
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FURRY, W. Number of Primes and Probability Considerations. Nature 150, 120–121 (1942). https://doi.org/10.1038/150120a0
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DOI: https://doi.org/10.1038/150120a0
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